Fishtank Learning

8th Grade Math
Unit 7: Pythagorean Theorem and Volume
Lesson 6

Objective

Understand the Pythagorean Theorem as a relationship between the side lengths in a right triangle.

Anchor Problems - Problem 1

Several right triangles are shown below (not drawn to scale). In a right triangle, the two side lengths that form the right angle are called legs, and the side length opposite the right angle is called the hypotenuse. 

Use the triangles to investigate the question: What relationship do you see between the measures of the legs and the measure of the hypotenuse?

Anchor Problems - Problem 2

Use the Pythagorean Theorem to show the relationship between the sides of the right triangles shown below.

Anchor Problems - Problem 3

A right triangle has side lengths $$6$$ units, $$4$$ units, and $${\sqrt{20}}$$ units. 

Which side length represents the hypotenuse?

Problem Set

Target Task - Problem 1

Lee tried to use the Pythagorean Theorem on the triangle shown below and found that the relationship did not hold true. 


Explain why the Pythagorean Theorem did not show a true relationship in Lee’s triangle. 

Target Task - Problem 2

Which three measures could be the side lengths of a right triangle? Explain or show your reasoning.

$$5$$                $$2$$                $$7$$               $$\sqrt{24}$$