Geometry

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Credits: 1

Prerequisite: Algebra 1

Recommended: 9th, 10th

Test Prep: SAT, PSAT 

Course Description: This high school geometry course moves students from the basic principles of geometry through more advanced topics such as fractals. Students learn through textbooks, videos, practice, investigations, and online interactives. Students will complete exams, including a midterm and a final. Topics covered in this course include properties of lines and angles, symmetry and transformations, reasoning and proofs, congruent triangles, properties of triangles and quadrilaterals, similar triangles, Pythagorean theorem and trigonometric ratios in right triangles, properties of circles, perimeter and area of 2-dimensional figures, surface area and volume of 3-dimensional solids, coordinate geometry including equations of lines and circles, constructions, and probability.

Honors Option: The workbook has extra work labeled as “Honors” for students who want to put in the extra work for the recognition. Here is the honors packet of extra work for online, buy or print. This version has space for working on the page and includes the answers. In the lessons, this is linked, but just for viewing online to copy the problems down.

Materials: protractor, ruler, drawing compass, drawing paper, graph paper

Resources: a variety of links to videos and readings as well as EP created worksheets

Books

Go here to learn about the OFFLINE course books (Workbook + Answers)

For the ONLINE course, you can add the optional HONORS packet of extra work: buy or print. (As an Amazon Associate I earn from qualifying purchases.)

 

Algebra Review

Lesson 1* (an asterisk indicates there is something to print)

  1. If you didn’t get here through My EP Assignments, I suggest you go there and create an account.
  2. This course is available completely offline. Click here for more information if you’re interested in the offline version.
  3. *Print out your first quarter grading sheet.
  4. This week we review algebra skills you’ll use in this course. If you find these reviews challenging, take time and go over related lessons in the Algebra 1 course.
  5. Remember how to simplify square root expressions? Watch or read.
  6. Simplify square root expressions. Do all problems.
  7. Remove radicals from the denominator. Do problems 1 through 5.
  8. Record 5 points on your grading sheet if you completed all of your assignments.
  9. Honors Option: The workbook has extra work labeled as “Honors” for students who want to put in the extra work for the recognition. Here is the honors packet of extra work for online, buy or print. The print/buy version has space for working on the page and has the answers. In the lessons, this worked is linked on the specific lessons but just for viewing online to copy the problems down.

Lesson 2

  1. Review solving two-step linear equations and multi-step linear equations.
  2. Solve two-step and multi-step linear equations. Do all problems.
  3. Review ways of solving proportions.
  4. Solve proportions. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 3

  1. Review writing slope-intercept equations.
  2. Write slope-intercept equations from a graph. Do all problems.
  3. Write slope-intercept equations from two points. Do all problems.
  4. Review equations of horizontal and vertical lines.
  5. Write equations of horizontal and vertical lines. Do all problems.
  6. Review graphing equations of lines using intercepts.
  7. Graph equations of lines in standard form. Do all problems.
  8. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 4

  1. Review solving systems of linear equations by substitution and by elimination.
  2. Solve systems of linear equations algebraically. Do all problems.
  3. Review solving systems of linear equations by graphing.
  4. Solve systems of linear equation graphically. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 5

  1. Review multiplying binomials. Watch or read.
  2. Review special binomial products. These patterns are worth memorizing. Write them down a couple of times.
  3. Multiply binomials. Do problems 1 through 4.
  4. Review three ways of solving quadratic equations. Write down the quadratic formula a couple of times.
  5. Solve quadratic equations by factoring. Do all problems.
  6. Solve quadratic equations by completing the square. Do all problems.
  7. Solve quadratic equations using the quadratic formula. Do all problems.
  8. Record 5 points on your grading sheet if you completed all of your assignments.

Geometry Basics

Lesson 6(*) (an asterisk in parentheses indicates there are pages that are optional to print)

  1. Go through basic terms and notations. Read aloud the definitions.
  2. Name basic geometric figures. Pause the video and work out each problem on your own.
  3. Interpret geometric diagrams. Do problems 1 through 18.
    • Answers are included in the worksheets.
    • Video solutions are also available: part 1 and part 2.
  4. (*)You may want to print these out and keep them handy.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 7

  1. Learn about basic postulates involving points, lines and planes. Be sure to Work out each problem on your own. (Answers to the last four problems: False, True, True, False)
  2. Learn about two addition postulates. Work out each problem on your own.
  3. Use the Segment Addition Postulate. Do problems 7 through 14. (Video solutions: part 1, part 2, part 3)
  4. Use the Angle Addition Postulate. Do problems 7 through 14. (Video solutions: part 1, part 2)
  5. Read about the parallel postulate.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 8

  1. Learn to classify angles by their measures.
  2. Classify angles by their measures. Do all problems.
  3. Learn about angle pairs formed by intersecting lines.
  4. Identify angle pairs and find angle measures. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 9

  1. Learn about angle pairs formed by parallel lines cut by a transversal. Click on “Learn with an Example” and just read, don’t worry about the practice.
  2. Identify the transversals. (If this throws a security error, it is SAFE to click to continue to the site.)
  3. Identify angle pairs and find angle measures. Do problems 1 through 24. (Video solutions: part 1, part 2)
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 10

  1. Learn to identify parallel lines and find angle measures that make lines parallel.
  2. Here are two images of what angles are congruent when two parallel lines are cut by a transversal.
  3. Find angle measures that make lines parallel. Do problems 1 through 16. (Video solutions: part 1, part 2)
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 11

  1. Learn to classify triangles by sides and angles.
  2. Classify triangles by both sides and angles. Do all problems.
  3. Learn about interior angles of triangles. Read aloud the theorem, then study the examples. Skip the proofs for now. You’ll prove this theorem in later lessons.
  4. Find interior angle measures of triangles.
  5. Learn about exterior angles of triangles. Read aloud the definition and the theorem, then study the examples. Skip the proof for now.
  6. Find exterior angle measures of triangles. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 12

  1. Read about quadrilaterals.
  2. Classify quadrilaterals. Do all problems.
  3. Learn about interior angles of quadrilaterals. Do the practice problems at the end of the video. (Answers: a) 100°, b) 150°, c) 160°, d) 63°, e) 31°, f) 128°, g) 24°, h) 65°, i) 68°)
  4. Learn about exterior angles of quadrilaterals. Do the practice problems at the end of the video. (Answers: a) 106°, b) 113°, c) 77°, d) 104°, e) 104°)
  5. Apply algebra to find angle measures. Do problems 15 through 18.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 13

  1. Read about polygons.
  2. Classify polygons. Do all problems.
  3. Learn about interior and exterior angles of polygons.
  4. Here are more examples. Skip if you are confident.
    • Check only examples you are not sure how to solve. Skip ones you can see how to solve. The important thing is that you understand. You may want to first do the practice problems below, then check back these examples if you got any problem wrong. Study efficiently!
  5. Practice with polygons. Do all problems.
  6. Practice with polygons. Do problems 2 through 10.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 14

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Geometry Basics. Here are activities you can use:

Transformations

Lesson 15

  1. Learn about symmetry.
  2. Identify reflectional symmetries. Do all problems.
  3. Identify rotational symmetries. Do all problems.
  4. Practice with symmetries. Do problems 1 through 6. Try all if you are up for a challenge!
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 16

  1. Refresh your memory on translations.
  2. Relate your understanding to geometry. Read the section “Translations.”
  3. Work out the examples on translations.
  4. Here are more examples. Skip if you are confident.
  5. Perform translations. Do all problems.
  6. Practice with translations. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 17

  1. Refresh your memory on reflections. Pay attention to how coordinates change.
  2. Relate your understanding to geometry. Read the section “Reflection in a Line.”
  3. Work out the examples on reflections.
  4. Here are more examples. Skip if you are confident.
  5. Perform reflections. Do all problems.
  6. Practice with reflections. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 18

  1. Refresh your memory on rotations. Pay attention to how coordinates change.
  2. Relate your understanding to geometry. Read the section “Rotations.”
  3. Work out the examples on rotations.
  4. Here are more examples (part 1, part 2). Skip if you are confident.
  5. Perform rotations of points. Do all problems.
  6. Perform rotations of polygons. Do all problems.
  7. Practice with rotations. Do all problems.
  8. Record 5 points on your grading sheet if you completed all of your assignments.
  9. If you are doing the Honors work, there is an extra assignment today.

Lesson 19

  1. Refresh your memory on dilations.
  2. Relate your understanding to geometry. Read through the page. Stop at “Dilation with Center NOT at Origin.”
  3. Here are more examples. Skip if you are confident.
  4. Perform dilations. Do all problems.
  5. Practice with dilations. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 20

  1. Read aloud the sentences below.
    • A rigid transformation is a transformation that does not change the size or shape of a figure.
    • A rigid transformation is also called an isometry.
    • Translations, reflections, and rotations are all rigid transformations.
    • A rigid transformation produces an image that is congruent to the preimage.
  2. Review properties of rigid transformations. Do all problems.
  3. Learn about compositions of rigid transformations.
  4. Work out the examples on naming compositions as a single transformation.
  5. Practice with compositions of rigid transformations. Do problems 1 through 9.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 21

  1. Read aloud the sentences below.
    • A similarity transformation is a dilation or a composition of dilations and rigid transformations.
    • A similarity transformation changes the size of a figure but not its shape.
    • A similarity transformation produces an image that is similar to the preimage.
  2. Work out the examples on identifying single transformations.
  3. Work out the examples on identifying composite transformations.
  4. Practice all you learned about transformations. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 22

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Transformations. Here are activities you can use:

Reasoning and Proofs

Lesson 23

  1. Learn about inductive reasoning, conjectures, and counterexamples. Be sure to Work out each problem on your own.
  2. Work out the examples on recognizing patterns. Just the Examples, not the Review problems.
  3. Use indicative reasoning to find patterns. Do all problems.
  4. Work out the examples on finding counterexamples. Don’t do the Review problems.
  5. Find counterexamples. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 24

  1. Learn about conditional statements.
  2. Write conditional statements. Do all Review problems at the bottom of the page, then check your answers. Study the examples on the page if you need more help.
  3. Learn about converse and biconditional statements.
  4. Write converse and biconditional statements. Do Review problems 5 through 10, then check your answers.
  5. Learn to apply deductive reasoning. Work out the examples on your own.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 25

  1. Copy the properties of equality and congruence in your notebook.
  2. Identify properties of equality. Do all problems.
  3. Play two matching quizzes: quiz 1 and quiz 2.
  4. Learn to write algebraic proofs using properties of equality.
  5. Solve equations and justify each step. Do all Review problems, then check your answers. (Answer Correction for #6: -2 * 3 should be -6, which would make the answer positive)
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 26

  1. Read about types of proofs. You don’t have to fully understand the examples yet. Just check out how each type looks like.
  2. Study four examples of proving statements about segments and angles.
  3. Complete algebraic proofs. Do all problems.
  4. Complete two-column proofs. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 27

  1. What is indirect proof (or proof by contradiction)?
  2. Study three more examples on indirect proof.
  3. Compare direct proofs and indirect proofs.
  4. Write an indirect proof of each statement below.
    • If 3x − 2 > 16, then x > 6.
    • If 7x − 4 is odd, then x is odd.
    • If △ABC is equiangular, then ∠A measures 60°.
    • If ABCDE is a regular hexagon, then ∠A is obtuse.
  5. Check your answers.
  6. Think about why we learn proofs. Check these out.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 28

  1. Review identifying transformations. Work out the examples on your own.
  2. Read aloud the sentences below.
    • A transformational proof uses transformations to prove that figures are congruent or similar
    • Two figures are congruent if and only if you can map one figure onto the other using rigid transformations (translations, reflections, and rotations).
    • Two figures are similar if and only if you can map one figure onto the other using a similarity transformation (a dilation or a composition of dilations and rigid transformations).
  3. Learn how to prove congruence using rigid transformations.
  4. Prove congruence using rigid transformations. Do all problems.
  5. Learn how to prove similarity using similarity transformations.
  6. Prove similarity using similarity transformations. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 29

  1. What is a theorem? Read the first section “The Building Blocks of Proofs.”
  2. Make sure you can answer these questions. Use the links to see the definitions if you need a reminder.
  3. Read aloud Postulate 29.1 and Theorems 29.1 through 29.4. This is a complete list of postulates and theorems you will learn in this course. You may want to print it out and keep it handy if you didn’t in lesson 6.
  4. See how you prove these theorems. Pause at each step and think about what comes next. Note that there is often more than one way to prove the given statement(s). The proof given here is just one possible way.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 30

  1. Make sure you can answer these questions. Use the links to see the definitions if you need a reminder.
  2. Read aloud Postulate 30.1 and Theorems 30.1 through 30.3.
  3. Prove these theorems. Pause at each step and say what comes next.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 31

  1. Are the lines parallel? Do a quick review.
  2. Read aloud Theorems 31.1 through 31.3.
  3. Read the section “Transitive Property of Parallel Lines.”
  4. Prove these theorems. Pause at each step and say what comes next.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 32

  1. Do a quick review on interior angles of polygons and exterior angles of polygons.
  2. Read aloud Theorems 32.1 through 32.4.
  3. Prove these theorems. Pause at each step and say what comes next.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 33

  1. Read aloud the postulate and the theorems listed below.
  2. You can prove geometric theorems using transformations. Here are some examples. Read the transformational proof on each page.
  3. Practice with proofs using transformations. Do all problems.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 34

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Reasoning and Proofs. Here are activities you can use:

Congruent Triangles

Lesson 35

  1. Learn about congruent triangles. Read the lesson and study the examples. NOTE: We’ll be using this site a lot. Don’t do the Review problems unless directed specifically. If your lesson just says, “Read and study the examples,” that means the Review questions are NOT assigned.
  2. Learn about congruence statements. Read and study the examples.
  3. Learn about the Third Angle Theorem. Read and study the examples.
  4. Practice with congruent triangles. Do all problems.
  5. Prove the theorem you just used. Pause at each step and say what comes next.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 36

  1. There are five shortcut methods to prove triangles congruent. You’ll learn the first two today. Read aloud Theorems 36.1 and 36.2.
  2. Learn about the SSS Congruence Theorem. Read and study the three examples: 4.13.2 through 4.13.4.
  3. Learn about the SAS Congruence Theorem. Read and study the examples.
  4. Here are more examples. Skip if you are confident.
  5. Identify SSS and SAS congruence. Do odd problems. (Video solutions: part 1, part 2)
  6. Work out three proofs using SSS and SAS. Pause at each step and say what comes next.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 37

  1. Learn two more shortcuts commonly used to prove triangles congruent. Read aloud Theorems 37.1 and 37.2.
  2. Learn about the ASA and AAS Congruence Theorems. Read and study the examples.
  3. Here are more examples. Skip if you are confident.
  4. Identify AAS and AAS congruence. Do odd problems. (Video solutions: part 1, part 2)
  5. Work out two proofs using ASA and AAS. Pause at each step and say what comes next.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 38

  1. Read aloud Theorem 38.1. This is the last shortcut to prove congruence of two triangles.
  2. Learn about the HL Congruence Theorem. Read and study the examples.
  3. Work out a proof using HL. Pause at each step and say what comes next.
  4. Here are more examples on congruence by HL and congruence by CPCTC. Skip if you are confident.
  5. Once you prove triangles congruent, you can say their parts congruent by CPCTC (Corresponding Parts of Congruent Triangles are Congruent). You’ll easily understand what this means once you see examples.
  6. Work out five proofs using CPCTC. Pause at each step and say what comes next.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 39

  1. Review SSS, SAS, ASA, and AAS congruence. Do all problems.
  2. Learn about congruence in overlapping triangles. (optional text lesson)
  3. Work out the first two proofs. Pause at each step and say what comes next.
  4. Try the third one if you are up for a challenge.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 40

  1. Read aloud Theorems 40.1 through 40.4.
  2. Learn about isosceles triangles. Read and study the examples.
  3. Learn about equilateral triangles. Read and study the examples.
  4. Practice with isosceles and equilateral triangles. Do problems 1 through 9. Do problem 10 if you are up for a challenge.
  5. Prove the theorems about isosceles and equilateral triangles. Pause at each step and say what comes next.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 41

  1. Why SSA and AAA are not congruence shortcuts? Read the section “Methods that DO NOT Prove Triangles Congruent.”
  2. Why the congruence shortcuts work? You can prove them using transformations. Read the first three proofs.
  3. Justify triangle congruence using transformations. Do all problems.
  4. You can prove AAS and HL using other congruence theorems. Pause at each step and say what comes next.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 42

  1. Read aloud the theorems involving congruent triangles: Theorems 35.1 through 40.4. Make sure you understand what each theorem means. If not, go back and check.
  2. Prove triangle congruence. Do all problems.
  3. Write proofs involving congruent triangles. Do the worksheet. (You can print the worksheets in this course if you’d like, but they’re intended to just be viewed on the screen and answered on separate paper.) Check your answers.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 43

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Congruent Triangles. Here are activities you can use:

Quarterly Review

Lesson 44

  1. Do the worksheets to review the first quarter. The problems marked “HONORS” are optional. Try them if you are up for a challenge.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 45

  1. Do the worksheets to review the first quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Properties of Triangles

Lesson 46*

  1. *Print out your second quarter grading sheet.
  2. Review angles in triangles. Do problems 1 through 6.
  3. Review angles and parallel lines. Do all problems.
  4. Learn about midsegments of triangles. Read aloud the definition and the theorem, then work out the examples. Don’t do the proofs.
  5. Here are more examples. Skip if you are confident.
  6. Practice with midsegments. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 47

  1. Study the section “Perpendicular Bisectors in a Triangle.” Read aloud the definition and the theorem(s), then work out the examples.
  2. Practice with perpendicular bisectors. Do Review problems 1 through 9, then check your answers. You don’t have to read the lesson or work through the examples unless you want to.
  3. Prove the theorems about perpendicular bisectors. Be sure to pause at each step and say what comes next.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 48

  1. Study the section “Angle Bisectors in a Triangle.” Read aloud the definition and the theorem(s), then work out the examples.
  2. Practice with angle bisectors. Do Review problems 1 through 9, then check your answers.
  3. Prove the theorems about angle bisectors. Pause at each step and say what comes next.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 49

  1. Study the section “Medians in Triangles.” Read aloud the definition and the theorem(s), then work out the examples.
  2. Work out all examples on medians and centroid.
  3. Here are more examples. Skip if you are confident.
  4. Practice with medians. Do problems 1 through 12. (Video solutions: part 1, part 2)
  5. Review midsegments of triangles. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 50

  1. Study the section “Altitudes in Triangles.” Read aloud the definition, then work out the examples.
  2. Work out all examples on altitudes.
  3. Practice with altitudes and medians. Do all problems.
  4. Review bisectors of triangles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 51

  1. Read aloud the theorems involving segments and centers of triangles: Theorems 46.1 through 49.1. Make sure you understand what each theorem means. If not, go back and check.
  2. Review segments and centers of triangles.
  3. Review midsegments of triangles. Do all problems.
  4. Review bisectors, medians, and altitudes of angles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 52

  1. Review solving one-step linear inequalities. Do all problems.
  2. Learn about inequalities in one triangle. Read aloud the theorems, then work out the examples.
  3. Work out all examples using the Triangle Inequality Theorem. Example 2 has the worked out solution for example 3. It should be simple enough for you to figure out, though. You know 4 + 4 is not greater than 8, right?
  4. Here are more examples. Skip if you are confident.
  5. Practice with inequalities in one triangle. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 53

  1. Review solving two-step linear inequalities. Do all problems.
  2. Learn about inequalities in two triangles. Read aloud the theorems, then work out the examples.
  3. Work out all examples comparing sides and angles in triangles.
  4. Compare sides and angles in triangles. Do all problems.
  5. Practice with inequalities in two triangles. Do problems 1 through 7.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 54

  1. Read aloud the theorems involving triangles: Theorems 46.1 through 53.2. Make sure you understand what each theorem means. If not, go back and check.
  2. Write proofs involving segments of triangles. Do the worksheets. Check your answers.
  3. Write proofs involving congruent triangles. Do problems 3 through 6.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 55

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Properties of Triangles. Here are activities you can use:

Properties of Quadrilaterals

Lesson 56

  1. Read aloud Theorems 56.1 through 56.4.
  2. Learn about parallelograms. Be sure to Work out each problem on your own. (optional text lesson)
  3. Here are more examples. Skip if you are confident.
  4. Find measures in parallelograms. Do all problems.
  5. Prove the theorems about parallelograms. Cover the table, then say what comes next before revealing each row. If you find it difficult, cover the Reasons column and justify each step.
    • Theorem 56.1: Parallelogram Opposite Sides Theorem
    • Theorem 56.2: Parallelogram Consecutive Angles Theorem (See the link above.)
    • Theorem 56.3: Parallelogram Opposite Angles Theorem (See the link above.)
    • Theorem 56.4: Parallelogram Diagonals Theorem (See the link above.)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 57

  1. Read aloud Theorems 57.1 through 57.4.
  2. Learn how to prove a quadrilateral is a parallelogram.
  3. Identify parallelograms. Do all problems.
  4. Prove the theorems about parallelograms. Cover the table, then say what comes next before revealing each row. If you find it difficult, cover the Reasons column and justify each step.
    • Theorem 57.1: Parallelogram Opposite Sides Converse
    • Theorem 57.2: Parallelogram Opposite Angles Converse (See the link above.)
    • Theorem 57.3: Parallelogram Diagonals Converse (See the link above.)
    • Theorem 57.4: Parallel Congruent Sides Theorem (See the link above.)
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 58

  1. Read aloud Theorems 58.1 through 58.3.
  2. Learn about special parallelograms. (optional text lesson)
  3. Here are more examples on rhombuses and rectangles. Skip if you are confident.
  4. Find measures in special parallelograms. Do all problems.
  5. Classify parallelograms. Do Review problems 4 through 15, then check your answers.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 59

  1. Read aloud Theorems 59.1 through 59.6.
  2. Learn about trapezoids. Read and study the examples.
  3. Learn about kites. Read and study the examples.
  4. Here are more examples on trapezoids and kites. Skip if you are confident.
  5. Find measures in trapezoids and kites. Do all problems.
  6. Find measures in quadrilaterals. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 60

  1. Read aloud the theorems involving quadrilaterals: Theorems 56.1 through 59.6. Make sure you understand what each theorem means. If not, go back and check.
  2. Prove parallelogram properties. Do all problems.
  3. Write proofs involving quadrilaterals. Do the worksheet. Check your answers.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 61

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Properties of Quadrilaterals. Here are activities you can use:

Similar Triangles

Lesson 62

  1. Review solving proportions. Do all problems.
  2. Learn about similar polygons. Be sure to Work out each problem on your own. (optional text lesson)
  3. Identify similar polygons. Do problems 1 through 10. (Video solutions: part 1)
  4. Find missing sides in similar polygons. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 63

  1. There are three shortcut methods to prove triangles similar. You’ll learn the first one today. Read aloud Theorem 63.1.
  2. Learn about AA similarity. (optional text lesson)
  3. Identify similar triangles by AA. Do all problems.
  4. Identify or solve similar triangles. Do problems 6 through 21, then check your answers.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 64

  1. Review solving rational equations. Do all problems.
  2. Read aloud Theorem 64.1. This is the second shortcut to prove triangles similar.
  3. Learn about SSS similarity. (optional text lesson)
  4. Identify similar triangles by SSS. Do all problems.
  5. Find missing sides in similar triangles. Do problems 13 through 20. (Video solutions: part 2)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 65

  1. Read aloud Theorem 65.1. This is the last shortcut to prove triangles similar.
  2. Learn about SAS similarity. (optional text lesson)
  3. Identify similar triangles. Do all problems.
  4. Read about types of similarity problems.
  5. Find missing sides and angles in similar triangles. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 66

  1. Read aloud the three similarity theorems: Theorems 63.1 through 65.1.
  2. Review proving similarity using transformations. Do all problems.
  3. Why the similarity shortcuts work? You can prove them using transformations. Read or watch.
  4. Prove triangle similarity. Do all problems.
  5. Find missing sides in similar triangles. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 67

  1. Do a quick review on simplifying radicals. Just four problems!
  2. Read aloud Theorem 67.1.
  3. Learn about similarity in right triangles. Read the first theorem and the explanation below it. You will learn the rest tomorrow.
  4. Work out the examples on similar right triangles.
  5. Find missing sides in similar right triangles. Do odd problems. (Video solutions: part 1, part 2)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 68

  1. Review solving quadratics by taking square roots. Do problems 1 through 6.
  2. Read aloud Theorems 68.1 and 68.2.
  3. Learn about geometric means and similar right triangles. (optional text lesson, second text lesson)
  4. Here are more examples. Skip if you are confident.
  5. Find missing sides in similar right triangles. Do problems 1 through 12.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 69

  1. Read aloud Theorems 69.1 and 69.2.
  2. Learn about proportional parts in triangles parallel lines. (optional text lesson)
  3. Here are more examples. Skip if you are confident.
  4. Find missing sides in triangles and parallel lines. Do problems 1 through 10. (Video solutions: part 1, part 2)
  5. Find missing sides in triangles with side splitters. Do problems 1 through 9.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 70

  1. Read aloud Theorem 70.1.
  2. Learn about proportions with angle bisectors. Skip the proof.
  3. Work out three more examples on angle bisectors and proportions.
  4. Find missing sides in triangles with angle bisectors. Do problems 13 through 18. (Video solutions: part 3)
  5. Find missing sides in triangles with angle bisectors. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 71

  1. Read aloud the theorems involving similar triangles: Theorems 63.1 through 70.1. Make sure you understand what each theorem means. If not, go back and check.
  2. Read about types of proof problems involving similar triangles.
  3. Write proofs involving similar triangles. Do all problems.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 72

  1. Here are six application problems involving similar triangles and proportions. Work out each problem on your own before checking the solution.
  2. Now exercise all your skills on similar triangles. Do all problems.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 73

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Similar Triangles. Here are activities you can use:

Right Triangles & Trigonometry

Lesson 74

  1. Read aloud Theorem 74.1.
  2. Learn about the Pythagorean theorem.
  3. Read about Pythagorean triples.
  4. Here are more examples. Skip if you are confident.
  5. Find missing sides in right triangles. Do all problems.
    • For problem 17, remember that the diagonals of a rhombus are perpendicular.
  6. There are many ways to prove the Pythagorean Theorem. Watch if you are interested.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 75

  1. Read aloud Theorems 75.1 through 75.3.
  2. Learn to classily triangles using Pythagorean inequalities. (optional text lesson)
  3. Here are more examples. Skip if you are confident.
  4. Practice with the Pythagorean theorem and inequalities. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 76

  1. Read aloud Theorems 76.1 and 76.2.
  2. Learn about 30-60-90 triangles. Read and study the examples.
  3. Learn about 45-45-90 triangles. Read and study the examples.
  4. Here are more examples. Skip if you are confident.
  5. Find missing sides in 30-60-90 triangles. Do all problems.
  6. Find missing sides in 45-45-90 triangles. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 77

  1. Review special right triangles. Do all problems.
  2. Learn about three basic trigonometric ratios.
  3. You can use a calculator to find trigonometric ratios.
    • Make sure your calculator is in degree (DEG) mode, not in radian (RAD) mode.
    • If you don’t have a scientific calculator, use an online calculator or an app.
  4. Find trigonometric ratios in right triangles. Do all problems. (The second to last question, the last picture question, the bottom row should be finding Z not Y. sinZ, cosZ, tanZ  The numbers on the problem are 32, 40, 24 and Z is at the top of the triangle in the image.)
  5. You can use special right triangles to find trigonometric ratios of 30, 45, and 60. Complete the table before checking the answers.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 78

  1. Review finding trigonometric ratios in right triangles. Do all problems.
  2. Learn about sines and cosines of complementary angles.
  3. Practice with sines and cosines of complementary angles. Do problems 1 through 6.
  4. Learn about solving for a side in right triangles.
  5. Here are more examples. Skip if you are confident.
  6. Solve for a side in right triangles. Do problems 1 through 8. (Video solutions: part 1)
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 79

  1. Review solving for a side in right triangles. Do all problems.
  2. Learn about inverse trigonometric ratios.
  3. Here are more examples. Skip if you are confident.
  4. Solve for an angle in right triangles. Do odd problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 80

  1. Review solving for an angle in right triangles. Do all problems.
  2. Learn to solve right triangles (or find all sides and angles).
  3. Solve for a side or an angle in right triangles. Do problems 1 through 8. Do all if you are up for a challenge.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 81

  1. Review solving for a side or an angle in right triangles. Do all problems.
  2. Learn to find areas of triangles using trigonometry. Stop at the section “Deriving this formula.”
  3. Practice with areas of triangles using trigonometry. Do all problems.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 82

  1. Learn to solve application problems using right triangle trigonometry.
  2. Here are more examples on angle of elevation and angle of depression. Skip if you are confident.
  3. Solve application problems using right triangle trigonometry. Do all problems.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 83

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Right Triangles & Trigonometry. Here are activities you can use:

Quarterly Review

Lesson 84

  1. Do the worksheets to review the first quarter. The problems marked “HONORS” are optional. Try them if you are up for a challenge.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 85

  1. Do the worksheets to review the second quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 86

  1. Do the worksheets to review the second quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Midterm Exam

Lesson 87

  1. There is a midterm exam in Lesson 90. A practice test is available in Lesson 89 to help you get ready. You can take the practice test any time before the exam.
  2. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  3. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 88

  1. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  2. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 89

  1. This is a practice test for your midterm exam. It is usually a good practice to take a practice test just like a real exam. Read the directions below in Lesson 90.
  2. When you are ready, take your practice test.
  3. Check your answers and review what you missed.

Lesson 90

  1. Before the test:
    • Take 10 minutes to review your notes.
    • Get a calculator and blank sheets of paper for your calculations.
  2. Keep in mind:
    • There are 30 questions on the test.
    • You may use a calculator throughout the exam.
    • Write your answers clearly in the space given. Do your work on separate paper.
    • There is no time limit, but you must complete the test in ONE sitting.
  3. When you are ready, take your midterm exam.
  4. After the test:
    • Grade your exam. Calculate and record your score out of 30.
    • Save your work for your portfolio. Save your exam.

Circles

Lesson 91*

  1. * Print your third quarter grading sheet.
  2. Learn about parts of circles. Read aloud each definition.
  3. Learn about tangent lines and circumscribed polygons. Read the theorems aloud as you watch.
  4. Here are more examples. Skip if you are confident.
  5. Practice with tangent lines. Do all problems. (Video solutions: part 1, part 2)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 92

  1. Review tangent lines. Do all problems.
  2. Read aloud the definitions below.
    • Congruent circles are circles with congruent radii.
    • Congruent arcs are arcs of the same circle or of congruent circles with equal measures.
  3. Learn about arcs and central angles. Read and study the examples.
  4. Read aloud Theorem 92.1 and Postulate 92.1.
  5. Here are more examples. Skip if you are confident.
  6. Practice with arcs and central angles. Do problems 5 through 18. (Video solutions: part 1, part 2)
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 93

  1. Review arc measures. Do all problems.
  2. Learn about chords. Read aloud the theorems and study the examples.
  3. Here are more examples. Skip if you are confident.
  4. Practice with chords. Do Review problems 8 through 22, then check your answers.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 94

  1. Review the theorems about chords. Read them aloud. Check the proofs if you are interested.
  2. Here are more examples. Skip if you are confident.
  3. Practice with chords. Do problems 1 through 8.
  4. Practice with arc and chords. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 95

  1. Learn about inscribed angles. Read and study the examples. Read the theorems aloud as you read.
  2. Here are more examples. Skip if you are confident.
  3. Practice with inscribed angles. Do Review problems 5 through 13, then check your answers. Note! On the answer key, the answers for 6 and 7 are reversed.
  4. Practice with central and inscribed angles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 96

  1. Review inscribed angles. Do all problems.
  2. Learn about inscribed quadrilaterals. Read and study the examples. Read the theorems aloud as you read.
  3. Here are more examples. Skip if you are confident.
  4. Practice with inscribed angles and polygons. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 97

  1. Learn about angles on and inside circles. Read and study the examples. Read the theorems aloud as you read.
  2. Here are more examples on chord-tangent angles and chord-chord angles. Skip if you are confident.
  3. Practice with angles on and inside circles. Do all problems.
  4. Practice with inscribed quadrilaterals. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 98

  1. Learn about angles outside circles. Read and study the examples. Read the theorems aloud as you read.
  2. Here are more examples. Skip if you are confident.
  3. Practice with angles outside circles. Do all problems.
  4. Practice with tangents and angles in circles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 99

  1. Learn about segments of circles. Read the theorems aloud as you watch. (optional text lesson 1, 2)
  2. Here are more examples (part 1 and part 2). You may want to check out examples that require solving quadratic equations. Skip if you are confident.
  3. Practice with segments of circles. Do all problems.
  4. Do more practice with segments of circles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 100

  1. Review angle of circles. Read the theorems aloud.
  2. Review segments of circles. Read the theorems aloud. Check the proofs if you are interested.
  3. Here more examples on angles on and inside circles, angles outside circles, chord-chord segments, secant-secant segments, and secant-tangent segments. Skip if you are confident.
  4. Practice with angles of circles. Do problems 1 through 8. (Video solutions: part 1)
  5. Practice with segments of circles. Do problems 1 through 8. (Video solutions: part 1)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 101

  1. Read aloud the theorems involving congruent triangles: Theorems 91.1 through 99.3. Make sure you understand what each theorem means. If not, go back and check.
  2. Learn how to prove that all circles are similar.
  3. Write proofs involving circles. Do all problems.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 102

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Circles. Here are activities you can use:

Perimeters and Areas

Lesson 103

  1. Learn to find areas of triangles and quadrilaterals. (optional text lesson)
  2. Find areas of parallelograms. Do all problems.
  3. Find areas of triangles. Do all problems.
  4. Find areas of trapezoids. Do all problems.
  5. Find perimeters and areas of rhombuses and kites. Do Review problems 8 through 11, then check your answers.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 104

  1. Review special right triangles. Do all problems.
  2. Review interior angles of polygons. Do problems 1 and 2.
  3. Learn to find areas of regular polygons. (optional text lesson)
  4. Find areas of regular polygons. Do problems 1 through 14. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 105

  1. Review finding missing sides in similar polygons. Do all problems.
  2. Learn about perimeters and areas of similar polygons. (optional text lesson)
  3. Find missing measures of similar polygons. Do Review problems 9 through 22, then check your answers.
  4. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 106

  1. Review arc measures. Do all problems.
  2. Remember what π is and how to find circumference?
  3. Learn to find arc length. Stop at Radian Measure.
  4. Here are more examples. Skip if you are confident.
  5. Practice with arc length. Do all Review problems, then check your answers.
  6. Try these arc length challenges. Do all four problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 107

  1. Review arc lengths. Do all problems.
  2. Remember how to find area of a circle?
  3. Learn to find areas of sectors and segments.
  4. Here are more examples. Skip if you are confident.
  5. Practice with sectors and segments. Do all Review problems, then check your answers. ANSWER CORRECTIONS for #4-8 are below. Highlight to see.
    4) 7.5 pi
    5) 1188 pi
    6) 13.86
    7) 30
    8) 15
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 108

  1. Learn about radians. Read the section “Radian Measure.”
  2. Convert between radians and degrees. Do all problems.
  3. Learn to find arc lengths and sector areas using radians. (optional text lesson 1, 2)
  4. Find arc lengths using radians. Do all problems.
  5. Find sector areas using degrees or radians. Do all problems.
  6. Try these arc length challenges. Do all three problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 109

  1. Review areas of sectors. Do all problems.
  2. Learn to find areas of composite figures. (optional text lesson 1, 2)
  3. Here are more examples (part 1, part 2). Skip if you are confident.
  4. Find areas of composite figures. Do all problems.
  5. Find areas of shaded regions. Do all problems.
  6. Find areas of composite figures involving circles. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 110

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Perimeters and Areas. Here are activities you can use:

Surface Areas and Volumes

Lesson 111

  1. Learn about polyhedrons.
  2. Identify parts of solids. Do all problems.
  3. Identify solids. Do all problems.
  4. Identify nets of solids. Do all problems.
  5. Practice with polyhedrons. Do all Review problems, then check your answers.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 112

  1. Review areas of regular polygons. Do problems 1 and 3.
  2. Learn to find surface areas of prisms and cylinders. (optional text lesson 1, 2)
  3. Here are more examples. Skip if you are confident.
  4. Find surface areas of prisms and cylinders. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 113

  1. Review areas of sectors and segments. Do problems 1 and 3.
  2. Learn to find surface areas of pyramids and cones. (optional text lesson 1, 2)
  3. Here are more examples on surface areas of pyramids and surface areas of cones. Skip if you are confident.
  4. Find surface areas of pyramids and cones. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 114

  1. Review areas of regular polygons. Do problems 2 and 4.
  2. Read about Cavalieri’s Principle.
  3. Apply Cavalieri’s Principle. Do all problems.
  4. Learn to find volumes of prisms and cylinders. (optional text lesson 1, 2)
  5. Here are more examples. Skip if you are confident.
  6. Find volumes of prisms and pyramids. Do problems 1 through 10. (Video solutions: part 1, part 2)
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 115

  1. Review areas of sectors and segments. Do problems 2 and 4.
  2. Learn to find volumes of pyramids and cones. (optional text lesson 1, 2)
  3. Here are more examples. Skip if you are confident.
  4. Find volumes of pyramids and cones. Do all problems. (Video solutions: part 1, part 2)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 116

  1. Review volumes of cylinders. Do all problems.
  2. Review volumes of cones. Do all problems.
  3. Learn to find surface areas and volumes of spheres.
  4. Read about how these sphere formulas are derived if you are interested.
  5. Here are more examples. Skip if you are confident.
  6. Find surface areas and volumes of spheres. Do odd problems. (Video solutions: part 1, part 2)
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 117

  1. Review perimeters and areas of similar polygons. Do problems 1 through 3.
  2. Learn about measurements in similar solids.
  3. Find missing measures of similar solids. Do all problems. (Video solutions: part 1, part 2)
  4. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 118

  1. Review the formulas for surface area and volume if you need.
  2. Learn to find surface areas and volumes of composite solids.
  3. Find volumes of composite solids. Do Review problems 1 through 3 and 14 through 22, then check your answers. Study the examples on the page if you need more help.
  4. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 119

  1. Learn about cross sections and solids of revolutions.
  2. Here are more examples. Skip if you are confident.
  3. Identify cross sections of solids. Do all problems.
  4. Related 2D shapes in 3D. Do all problems.
  5. Practice with solids of revolutions. Do Review problems 1 through 12, then check your answers.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 120

  1. Learn to apply volumes of solids.
  2. Solve volume word problems. Do all problems.
  3. Learn to apply surface areas of solids.
  4. Solve surface area word problems. Do all problems.
  5. Learn about area density.
  6. Learn about volume density.
  7. Solve density word problems. Do all problems.
  8. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 121

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Surface Areas and Volumes. Here are activities you can use:

Coordinate Geometry

Lesson 122

  1. Review the Pythagorean theorem. Do all problems.
  2. Learn about the distance formula.
  3. Practice using the distance formula. Do all problems.
  4. Learn about the midpoint formula.
  5. Practice using the midpoint formula. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 123

  1. Review the distance formula. Get four problems
  2. Review the midpoint formula. Do all problems.
  3. Learn to partition line segments. (optional text lesson)
  4. Here are more examples. Skip if you are confident.
  5. Practice partitioning line segments. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 124

  1. Review finding slopes from equations. Do all problems.
  2. Review writing equations in any form. Do all problems.
  3. Learn about equations of parallel and perpendicular lines. (optional text lesson)
  4. Here are more examples on identifying parallel and perpendicular lines and writing equations of parallel and perpendicular lines. Skip if you are confident.
  5. Practice with parallel and perpendicular lines. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 125

  1. Review solving systems of equations graphically. Do all problems.
  2. Review equations of parallel and perpendicular lines. Do all problems.
  3. Learn to find the distance between a point and a line.
  4. Learn to find the distance between two parallel lines.
  5. Find the distance between a point and a line. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 126

  1. Review the distance formula. Get four problems
  2. Review slopes of parallel and perpendicular lines. Do all problems.
  3. Learn to find areas on the coordinate plane.
  4. Find areas and perimeters on the coordinate plane. Do all problems.
  5. Learn to classify figures with coordinates.
  6. Classify figures by coordinates. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 127

  1. Learn about standard equations of circles. Read and study the examples.
  2. Graph a circle from its features. Do all problems.
  3. Identify features of a circle from its graph. Do all problems.
  4. Identify features of a circle from its standard equation. Do all problems.
  5. Graph a circle from its standard equation. Do all problems.
  6. Write standard equation of a circle. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 128

  1. Review completing the square. Do all problems.
  2. Learn about general equations of circles. Read about “General Form” and study the examples.
  3. Graph a circle from its expanded equation. Do all problems.
  4. Practice with equations of circles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 129

  1. Learn about coordinate proofs.
  2. Practice with coordinate proofs. Do all problems.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 130

  1. Read about coordinate proofs with variables.
  2. Read aloud the theorems listed below to remind you of what they are.
  3. Write coordinate proofs. Try to work out each problem on your own.
  4. Record 5 points on your grading sheet if you completed all of your assignments.
  5. If you are doing the Honors work, there is an extra assignment today.

Lesson 131

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Coordinate Geometry. Here are activities you can use:

Quarterly Review

Lesson 132

  1. Do the worksheets to review the first quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 133

  1. Do the worksheets to review the second quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 134

  1. Do the worksheets to review the third quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 135

  1. Do the worksheets to review the third quarter.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Constructions

Lesson 136*

  1. *Print your fourth quarter grading sheet.
  2. Read about construction.
  3. Get the following tools.
    • Compass: Check out ways to draw a circle without a compass if you don’t have one.
    • Straightedge: You can use a ruler but all markings must be ignored.
    • Ruler: You will use it to check your work.
    • Protractor: You will use it to check your work.
  4. Learn to construct congruent segments. (optional text lesson)
  5. Learn to construct congruent angles. (optional text lesson)
  6. Construct congruent segments. Do problems 1 through 4. (Video solutions: all problems)
    • You don’t need to print out these worksheets. For each problem, draw a diagram similar to the given one and do the construction.
    • After the construction, always check your work with a ruler and a protractor.
  7. Construct congruent angles. Do problems 1, 3, 4, and 5. (Video solutions: all problems)
  8. Record 5 points on your grading sheet if you completed all of your assignments.
  9. If you are doing the Honors work, there is an extra assignment today.

Lesson 137

  1. Learn to construct perpendicular bisectors.
  2. Learn to construct angle bisectors. (optional text lesson)
  3. Construct perpendicular bisectors. Do problems 5, 7, and 8. (Video solutions: all problems)
  4. Construct angle bisectors. Do problems 1 through 4. (Video solutions: all problems)
  5. Practice with proofs involving segments and angles. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 138

  1. Learn to construct parallel lines through a point. (optional text lesson)
  2. Learn to construct perpendicular lines through a point. (optional text lesson)
  3. Construct parallel and perpendicular lines. Do problems 9 through 12. (Video solutions: all problems)
  4. Practice with constructions. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 139

  1. Learn to construct equilateral triangles. (optional text lesson)
  2. Learn to construct squares. (optional text lesson)
  3. Learn to construct special angles. (optional text lesson)
  4. Do each construction on your own. Use only a compass and a straightedge. Check your work with a ruler and a protractor.
    • Construct an angle of 15 degrees. Here are the steps if you need help.
    • Construct an angle of 150 degrees. Here are the steps if you need help.
    • Construct a 45-45-90 isosceles right triangle. Here are the steps if you need help.
  5. Practice with constructions. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 140

  1. Learn to construct inscribed squares. (optional text lesson)
  2. Learn to construct inscribed regular hexagons. (optional text lesson)
  3. Do each construction on your own. Use only a compass and a straightedge. Check your work with a ruler and a protractor.
    • Construct a regular octagon inscribed in a circle. Here are the steps if you need help.
    • Construct an equilateral triangle inscribed in a circle. This is very similar to the construction of an inscribed hexagon. Just use every other vertex to form a triangle. Here are the steps if you need help.
  4. Practice with constructions. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 141

  1. Learn to construct the circumcenter of a triangle. (optional text lesson)
  2. Learn to construct the incenter of a triangle. (optional text lesson)
  3. Learn to construct the centroid of a triangle. (optional text lesson)
  4. Learn to construct the orthocenter of a triangle. (optional text lesson)
  5. Do each construction on your own. Use only a compass and a straightedge. Check your work with a ruler and a protractor.
    • Construct a right triangle. Here are the steps if you need help.
    • Construct the circumcenter of your triangle. If your construction is correct, then your circumcenter will be on the hypotenuse. Here are the steps if you need help.
    • Construct an obtuse triangle and its orthocenter. If your construction is correct, then your orthocenter will be outside the triangle. Here are the steps if you need help.
  6. Review points of concurrency. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.
  8. If you are doing the Honors work, there is an extra assignment today.

Lesson 142

  1. Learn to construct a tangent to a point on a circle.
  2. Learn to construct a tangent from a point outside a circle. (optional text lesson)
  3. Do each construction on your own. Use only a compass and a straightedge. Check your work with a ruler and a protractor.
    • Draw a circle of any radius. Take a point anywhere on your circle. Construct a tangent to the circle at the point.
    • Draw a circle of any radius. Take a point anywhere outside your circle. Construct two tangents to the circle from the point. If your construction is correct, then the two tangents will have equal lengths.
  4. Review tangents to circles. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 143

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Constructions. Here are activities you can use:

Probability

Lesson 144

  1. What is probability? Watch or read if you need a reminder.
  2. Find simple probability. Do problems 1 through 5.
  3. What is experimental probability? Watch or read if you need a reminder.
  4. Find theoretical and experimental probability. Do all problems.
  5. Learn about the complementary rule of probability.
  6. Find experimental probability and complementary probability. Do all problems.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 145

  1. Review simple probability. Do all problems.
  2. Review basic probability terms. Read aloud each definition.
  3. Review sample spaces and tree diagrams if you need a reminder.
  4. Review the counting principle if you need a reminder. (optional text lesson)
  5. Count outcomes of events. Do all problems. Be sure to pause the video and work out each problem on your own.
  6. Here is another counting problem with various conditions: Count the number of 4-letter codes from 6 letters with various conditions. Do the problem on your own.
  7. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 146

  1. Review the counting principle. Do all problems.
  2. Learn about probability of independent events.
  3. Find probability of independent events. Do all problems.
  4. Do more practice with independent probability. Do all problems.
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 147

  1. Review independent probability. Do all problems.
  2. Learn about probability of independent and dependent events.
  3. Find probability with and without replacement. Do all problems on your own.
  4. Do more practice with independent and dependent probability. Do problems 1 through 8. (Video solutions: part 1)
  5. Record 5 points on your grading sheet if you completed all of your assignments.
  6. If you are doing the Honors work, there is an extra assignment today.

Lesson 148

  1. Review dependent probability. Do all problems.
  2. Learn about probability of mutually exclusive (or disjoint) and overlapping events.
  3. Remember, you can always find probability by count outcomes instead of using the formula. Compare the two examples below.
  4. Find mutually exclusive and overlapping probability. Do all problems on your own.
  5. Do more practice with mutually exclusive and overlapping probability. Do problems 1 through 8. (Video solutions: part 1)
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 149

  1. Review the complement rule of probability. Be sure to understand the examples.
  2. Review the multiplication rule of probability. Be sure to understand the examples.
  3. Review the addition rule of probability. Be sure to understand the examples.
  4. Find “AND” and “OR” probability. Do all problems.
  5. Sometimes it is just easier to count outcomes. Do all problems on your own.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 150

  1. Learn about sets and Venn diagrams.
  2. Perform basic set operations. Do all problems.
  3. Learn about probability with sets.
  4. Find probability from Venn diagrams. Do all problems.
  5. Find probability involving sets. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 151

  1. Learn about two-way tables.
  2. Create two-way tables. Do all problems.
  3. Learn about probability with two-way tables.
  4. Find probability involving two-way tables. Do all problems.
  5. Find probability involving sets and two-way tables. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 152

  1. Learn about conditional probability.
  2. Find conditional probability. Do all problems.
  3. Learn to check for independence with conditional probabilities.
  4. Study another example. Skip if you are confident.
  5. Identify dependent and independent events. Do all problems.
  6. Record 5 points on your grading sheet if you completed all of your assignments.
  7. If you are doing the Honors work, there is an extra assignment today.

Lesson 153

  1. Review shaded area. Do all problems.
  2. Learn about geometric probability involving lengths.
  3. Learn about geometric probability involving areas. (optional text lesson)
  4. Find probability involving lengths and areas. Do all problems on your own.
  5. Here are five more real-life problems. Do all problems on your own.
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 154

  1. Learn about probability distribution.
  2. Learn to find probabilities from a probability distribution.
  3. Find probabilities from a probability distribution. Do all problems.
  4. Learn about expected value.
  5. Find expected value. Do all problems.
  6. Learn to interpret expected value.
  7. Interpret expected value. Do all problems.
  8. Learn to calculate expected payoff.
  9. Find expected payoffs. Do all problems.
  10. Record 5 points on your grading sheet if you completed all of your assignments.
  11. If you are doing the Honors work, there is an extra assignment today.

Lesson 155

  1. Read the following sentences:
    • A permutation is an arrangement of items in a particular order.
    • A combination is an arrangement of items in which order does not matter.
  2. Find the number of permutations and combinations using the counting principle. Do all problems on your own. Stop at Formulas.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 156

  1. Do a real quick review on factorial.
  2. Learn about permutation formula. (optional text lesson)
  3. Learn about combination formula. (optional text lesson)
  4. Here are more examples on permutations and combinations. Skip if you are confident.
  5. Find the number of permutations and combinations using the formulas. Do all problems. (Video solutions: all problems)
  6. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 157

  1. Learn about probability with permutations and combinations.
  2. Find probability using permutations and combinations. Do all problems. (Video solutions: all problems)
  3. Record 5 points on your grading sheet if you completed all of your assignments.
  4. If you are doing the Honors work, there is an extra assignment today.

Lesson 158

  1. Catch up if you are behind. Review lessons that caused you trouble.
  2. If you don’t need to catch up, review the section Constructions. Here are activities you can use:

Review: All Topics in Geometry

Lesson 159

  1. It is time for the end-of-year review. You will be solving two pages of review for each section. Worked-out answers are attached.
  2. Some worksheets have problems marked “HONORS.” They are optional. Try them if you are up for a challenge.
  3. Do the worksheets to review the section Geometry Basics.
  4. Check your answers. Review what you missed and why.
  5. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 160

  1. Do the worksheets to review the section Transformations.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 161

  1. Do the worksheets to review the section Reasonings and Proofs.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 162

  1. Do the worksheets to review the section Congruent Triangles.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 163

  1. Do the worksheets to review the section Properties of Triangles.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 164

  1. Do the worksheets to review the section Properties of Quadrilaterals.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 165

  1. Do the worksheets to review the section Similar Triangles.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 166

  1. Do the worksheets to review the section Right Triangles & Trigonometry.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 167

  1. Do the worksheets to review the section Circles.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 168

  1. Do the worksheets to review the section Perimeters and Areas.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 169

  1. Do the worksheets to review the section Surface Areas and Volumes.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 170

  1. Do the worksheets to review the section Coordinate Geometry.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 171

  1. Do the worksheets to review the section Constructions.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 172

  1. Do the worksheets to review the section Probability.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 173

  1. Do the worksheets to review the 1st and 2nd quarters.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Lesson 174

  1. Do the worksheets to review the 3rd and 4th quarters.
  2. Check your answers. Review what you missed and why.
  3. Record 5 points on your grading sheet if you completed all of your assignments.

Final Exam

Lesson 175

  1. There is a final exam in Lesson 180. A practice test is available in Lesson 179 to help you get ready. You can take the practice test any time before the exam.
  2. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  3. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 176

  1. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  2. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 177

  1. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  2. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 178

  1. Study on your own. Review lessons that caused you trouble. Solve the questions you missed and understand why you missed them.
  2. Make notes of the kinds of questions you get wrong repeatedly or you struggle with. Try to make your notes simple and clear so that you can review them quickly right before the exam.

Lesson 179

  1. This is a practice test for your final exam. It is usually a good practice to take a practice test just like a real exam. Read the directions below in Lesson 180.
  2. When you are ready, take your practice test.
  3. Check your answers and review what you missed.

Lesson 180*

  1. Before the test:
    • Take 10 minutes to review your notes.
    • Get a calculator and blank sheets of paper for your calculations.
  2. Keep in mind:
    • There are 35 questions on the test.
    • You may use a calculator throughout the exam.
    • Write your answers clearly in the space given. Do your work on separate paper.
    • There is no time limit, but you must complete the test in ONE sitting.
  3. When you are ready, take your final exam.
  4. After the test:
    • Grade your exam. Calculate and record your score out of 35 on your grading sheet.
    • *Calculate your grade for the course. See the grading sheet for the details.
    • Save your work for your portfolio. Save your exam.
  5. Congratulations on completing Geometry!
  6. Take the polls below.

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