Pythagorean Theorem and Volume

Lesson 8

Math

Unit 7

8th Grade

Lesson 8 of 16

Objective


Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.

Common Core Standards


Core Standards

  • 8.G.B.6 — Explain a proof of the Pythagorean Theorem and its converse.

Criteria for Success


  1. Understand that by the converse of the Pythagorean Theorem, if, for the side lengths of a triangle, $${a^2+b^2=c^2}$$, then the triangle is a right triangle with hypotenuse $$c$$.
  2. Use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes


Problem 1

Read the examples of statements and their converses shown below. 

Statement Converse of Statement
If it is raining outside, then the ground is wet. If the ground is wet, then it is raining outside.
If an animal is a cat, it has 4 legs. If an animal has 4 legs, it is a cat.
If you are between the ages of 13 and 19, then you are a teenager. If you are a teenager, then you are between the ages of 13 and 19.
If a polygon has four right angles and four equal sides, then it is a square. If a polygon is a square, then it has four right angles and four equal sides.

a.   Which of the converse statements are true?

b.   The Pythagorean Theorem states: If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse, or $${a^2+b^2=c^2}$$. What is the converse statement of the Pythagorean Theorem?

c.   Do you think the converse of the Pythagorean Theorem is true?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

For each triangle below, determine if the triangle is a right triangle. If it is, label the right angle in the diagram. (Figures not drawn to scale.)

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 3

The triangle below is not a right triangle. 

Change the measurement of one of the side lengths to create a right triangle. Label the right angle in the diagram. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Is the triangle shown below a right triangle? Justify your answer. If it is, label the right angle in the diagram.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Find missing side lengths involving right triangles and apply to area and perimeter problems.

Lesson 9
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free