Lesson | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

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

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

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).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics®, and is ©2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) . OUR's 6-8 Math Curriculum is available at https://openupresources.org/math-curriculum/ .

Adaptations and updates to IM 6-8 Math v.360 are ©2024 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution-Noncommercial 4.0 International License (CC BY-NC 4.0).

Adaptations to add additional English language learner supports are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The second set of English assessments (marked as set “B”) are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0) .

Spanish translation of the “B” assessments are ©2020 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Navigation

6-8 Grade 8 Unit 8 Lesson 10

Gradeband

K-5 Math •6-8 Math 9-12 Math

Course

Grade 6 Grade 7 •Grade 8

Unit

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

Lesson

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 Lesson 16 Lesson 17 Lesson 18

K-5
6-8
9-12

Grade 6
Grade 7
Grade 8

Accelerated 6
Accelerated 7

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

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
Lesson 16
Lesson 17
Lesson 18

Settings

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 8, Lesson 10

The Converse

Grade 8

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. Side lengths for A are: 9, 12, 14. Side lengths for B are: 10, square root 50, square root 50. Side lengths for C are: 16,30,35. Side lengths for D are: 10, 10 point 5, 14 point 5. Side lengths for E are: 4, square root 3, square root 13.

to access Practice Problem Solutions.

Lesson 10 Resources

Student Materials

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 9: Finding Unknown Side Lengths

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 7: 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 5: 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.