# Lesson 7

A Proof of the Pythagorean Theorem

### Lesson Narrative

In the warm-up of this lesson, students study a diagram they will use to prove the Pythagorean Theorem. In the first activity they prove the Pythagorean Theorem using the diagram. Then they apply the Pythagorean Theorem in the next activity. The final activity before the cool down is an optional look at a transformational proof of the Pythagorean Theorem.

### Learning Goals

Teacher Facing

• Calculate an unknown side length of a right triangle using the Pythagorean Theorem, and explain (orally) the reasoning.
• Explain (orally) an area-based algebraic proof of the Pythagorean Theorem.

### Student Facing

Let’s prove the Pythagorean Theorem.

### Required Preparation

If you choose to do the optional activity, you will need the 5 cut-out shapes from the Making Squares blackline master used in the first lesson of this unit—1 set of 5 for every 2 students. You will also need copies of the A Transformational Proof blackline master—1 copy for every 2 students.

### Student Facing

• I can explain why the Pythagorean Theorem is true.