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Splash Screen. Five-Minute Check (over Lesson 5-2) Main Ideas and Vocabulary California Standards Key Concept: Writing an Indirect Proof Example 1: State Assumptions Example 2: Algebraic Proof Example 3: Real-World Example Example 4: Geometry Proof. Lesson 3 Menu. Do Now. Do Now.

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Lesson 3 menu

Five-Minute Check (over Lesson 5-2)

Main Ideas and Vocabulary

California Standards

Key Concept: Writing an Indirect Proof

Example 1: State Assumptions

Example 2: Algebraic Proof

Example 3: Real-World Example

Example 4: Geometry Proof

Lesson 3 Menu




Lesson 3 mi vocab

  • Use indirect proof with geometry.

  • indirect reasoning

  • indirect proof

  • proof by contradiction

Lesson 3 MI/Vocab



Lesson 3 cyp1

A.

B.

C.

D.

  • A

  • B

  • C

  • D

Lesson 3 CYP1


Lesson 3 cyp11

A.

B.

C.

D.

  • A

  • B

  • C

  • D

Lesson 3 CYP1


Lesson 3 cyp12

PLH.

A.

B.MLH  PLH

C.

D.

  • A

  • B

  • C

  • D

Lesson 3 CYP1


Lesson 3 cyp2

Given:

Write an indirect proof in the correct order.

Prove:

Part BAssume that

Part A The assumption leads to a contradiction. Therefore, the assumption that must be false, which means that must be true.

Indirect Proof:

Lesson 3 CYP2


Lesson 3 cyp21

Part C Substitute –3 for a in the inequality

Substitution

Multiply.

Add.

This is a contradiction because the denominator cannot be 0.

Lesson 3 CYP2


Lesson 3 cyp22

A. C, B, A

B. C, A, B

C. B, C, A

D. B, A, C

  • A

  • B

  • C

  • D

Lesson 3 CYP2


Lesson 3 cyp3

Given: David spent less than $135.

Prove: At least one of the sweaters x cost less than $32. That is,

SHOPPING David bought four new sweaters for a little under $135. The tax was $7, but the sweater costs varied. Show that at least one of the sweaters cost less than $32.

Which is the correct order for this indirect proof?

Lesson 3 CYP3


Lesson 3 cyp31

Indirect Proof:

Part B Assume that none of the sweaters cost less than $32.

Part A then the minimum total amount David spent is However, this is a contradiction since David spent less than $135.

Part C The assumption leads to a contradiction of a known fact. Therefore, the assumption that must be false. Thus, at least one of the sweaters cost less than $32.

Lesson 3 CYP3


Lesson 3 cyp32

A. A, C, B

B. B, A, C

C. B, C, A

D. C, B, A

  • A

  • B

  • C

  • D

Lesson 3 CYP3


Lesson 3 cyp4

Which is the correct order for this indirect proof?

Given:ΔABCwith side lengths 8, 10, and 12 as shown.

Prove:mC > mA

Lesson 3 CYP4


Lesson 3 cyp41

Indirect Proof:

Part A Assume that

Part CBy angle-side relationships, By substitution, This inequality is a false statement.

Part B Since the assumption leads to a contradiction, the assumption must be false. Therefore, mC > mA.

Lesson 3 CYP4


Lesson 3 cyp42

A. C, B, A

B. C, A, B

C. B, A, C

D. A, C, B

  • A

  • B

  • C

  • D

Lesson 3 CYP4