# Lesson 6

A Proof of the Pythagorean Theorem

### Lesson Narrative

The purpose of this lesson is for students to make sense of one proof of the Pythagorean Theorem (MP1). They begin by studying a diagram central to the proof, which was first encountered earlier in the year during their study of transformations. In the first activity they prove the Pythagorean Theorem using the diagram. Then they apply the Pythagorean Theorem to find unknown side lengths for a variety of right triangles. Also included in this lesson is an optional activity where students can make sense of a transformational proof of the Pythagorean Theorem.

### Learning Goals

Teacher Facing

• Apply the Pythagorean Theorem to determine unknown side lengths in right triangles.
• Understand a proof of the Pythagorean Theorem.

### Student Facing

Let’s prove the Pythagorean Theorem.

### Student Facing

• I can explain why the Pythagorean Theorem is true.
• If I know the lengths of two sides, I can find the length of the third side in a right triangle.
• When I have a right triangle, I can identify which side is the hypotenuse and which sides are the legs.