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6-8 Accelerated 7 Unit 8 Lesson 8

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 •Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15

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Accelerated 7

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Unit 6
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Lesson 14
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Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

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Unit 8, Lesson 8

The Converse

Accelerated 7

Practice

Problem 1

Student Task Statement

Which of these triangles are definitely right triangles? Explain how you know. (Note that not all triangles are drawn to scale.)

5 triangles labeled A, B, C, D, E.

to access Practice Problem Solutions.

Lesson 8 Resources

Student Materials Student Materials in Spanish

Problem 2

Student Task Statement

A right triangle has a hypotenuse of 15 cm. What are possible lengths for the two legs of the triangle? Explain your reasoning.

A right triangle with a hypotenuse of 15 cm. The other two legs are unlabeled.

to access Practice Problem Solutions.

Problem 3

ForLesson 7: A Proof of the Pythagorean Theorem

Student Task Statement

In each part, and represent the length (in units) of a leg of a right triangle, and represents the length of its hypotenuse. Find the unknown length, given the other two lengths.

to access Practice Problem Solutions.

Problem 4

ForLesson 6: Finding Side Lengths of Triangles

Student Task Statement

For which triangle does the Pythagorean Theorem express the relationship between the lengths of its three sides?

Triangles A, B, C, D. B is a right triangle.

A
B
C
D

to access Practice Problem Solutions.

Problem 5

ForLesson 8: Solving Any Linear Equation

Student Task Statement

Andre makes a trip to Mexico. He exchanges some dollars for pesos at a rate of 20 pesos per dollar. While in Mexico, he spends 9,000 pesos. When he returns, he exchanges his pesos for dollars (still at 20 pesos per dollar). He gets back the amount he started with. Find how many dollars Andre exchanges for pesos and explain your reasoning. If you get stuck, try writing an equation representing Andre’s trip using a variable for the number of dollars he exchanges.

to access Practice Problem Solutions.