Geometry 5-5 Indirect Proof

by Matthew Richardson

| 18 QuestionsNote from the author:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

1

1

20 pts

Solve It! The goal of this game is to fill in the empty squares with numbers. The numbers 1, 2, 3, and 4 must appear once in each row and once in each column. Complete the games on the canvas.

2

2

10 pts

Problem 1 Got It?

A

B

C

D

3

3

10 pts

Problem 1 Got It?

A

B

C

D

4

10 pts

Problem 2 Got It? Which two statements contradict each other?

I. △XYZ is acute.

II. △XYZ is scalene.

III. △XYZ is equiangular.

Statements I & II

Statements II & III

Statements I & III

5

10 pts

Problem 2 Got It? Reasoning: Statements I and II below contradict each other. Statement III is the negation of Statement I. Are statements II and III equivalent?

I. △ABC is scalene.

II. △ABC is equilateral.

III. △ABC is not scalene.

Yes

No

6

20 pts

Problem 3 Got It? Complete the proof on the canvas.

Given: 7(x + y) = 70 and x ≠ 4.

Prove: y ≠ 6.

7

7

10 pts

A

B

C

D

8

10 pts

Write a statement that contradicts the following statement. Draw a diagram to support your answer.

Lines a and b are parallel.

9

9

10 pts

Error Analysis: A classmate began an indirect proof as shown below. Explain and correct your classmate's error.

10

10 pts

Review Lesson 5-4: The distances from the centroid of a triangle to its vertices are 16 cm, 17 cm, and 18 cm. What is the length of the shortest median?

8

9

24

27

11

10 pts

Review Lesson 5-4: The orthocenter of isosceles △ABC lies outside the triangle and m∠A = 30. What are the measures of the other two angles? Select all that apply.

30

60

90

120

12

10 pts

Review Lesson 2-4: You think, "If I leave home at 7:10, I'll catch the 7:25 bus. If I catch the 7:25 bus, I'll get to school before class starts. I am leaving and it's 7:10, so I'll get to school on time." Which law of deductive reasoning are you using?

The Law of Detachment

The Law of Syllogism

13

10 pts

Review Lesson 1-7: Identify the shortest and longest sides of △ABC.

- side AB
- side BC
- side AC

- Shortest
- Longest

14

10 pts

Review Lesson 1-7: Identify the shortest and longest sides of △ABC.

- side AB
- side BC
- side AC

- Shortest
- Longest

15

10 pts

Vocabulary Review: Draw a line from each statement in Column A to one or more pictures that contradicts it in Column B.

16

10 pts

Use Your Vocabulary: Write indirect or indirectly to complete the sentence.

The __?__ way home from school takes a lot more time.

Respond with one word, no spaces.

17

10 pts

Use Your Vocabulary: Write indirect or indirectly to complete the sentence.

By finding the negation of a statement false, you __?__ prove the statement true.

Respond with one word, no spaces.

18

10 pts

Reflection: Math Success

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