Lesson objective: Extend understanding of the Pythagorean Theorem to include the converse, such as if \(a^2 +b^2 = c^2\) then we have a right triangle.

Students bring prior knowledge of proving the Pythagorean Theorem from 8.G.B.6. This prior knowledge is extended to include the converse of the theorem as students use the theorem to classify triangles into a group with right angles and a group without right angles. A conceptual challenge students may encounter is relating the converse of the theorem to the proof of the theorem.

The concept is developed through work with repeated reasoning, which reinforces the connection between the proof of the Pythagorean Theorem and its converse.

This work helps students deepen their understanding of numbers because the values of the square numbers must fit Pythagoras's equation in order for the triangle to be a right triangle.

Students engage in Mathematical Practice 6 (Attend to precision) as they use the equal sign consistently and appropriately to check for the Pythagorean relationship.

**Key vocabulary:**

- converse
- right triangle
- squared

**Special materials needed: **none