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.
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Anchor Problems


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

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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

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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

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Problem Set

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Target Task


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

Student Response

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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.

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Lesson 7

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Lesson 9

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

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