# 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.

### Learning Targets

### 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.

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