# Lesson 9

The Converse

### Lesson Narrative

This lesson guides students through a proof of the converse of the Pythagorean Theorem. Then students have an opportunity to decide if a triangle with three given side lengths is or is not a right triangle.

### Learning Goals

Teacher Facing

• Determine whether a triangle with given side lengths is a right triangle using the converse of the Pythagorean Theorem.
• Generalize (orally) that if the side lengths of a triangle satisfy the equation $a^2+b^2=c^2$ then the triangle must be a right triangle.
• Justify (orally) that a triangle with side lengths 3, 4, and 5 must be a right triangle.

### Student Facing

Let’s figure out if a triangle is a right triangle.

### Student Facing

• I can explain why it is true that if the side lengths of a triangle satisfy the equation $a^2+b^2=c^2$ then it must be a right triangle.
• If I know the side lengths of a triangle, I can determine if it is a right triangle or not.