Explain a proof of the Pythagorean Theorem and its converse

What you'll learn

1. State the Pythagorean Theorem precisely, identifying the hypotenuse and legs of a right triangle and the relationship a^2 + b^2 = c^2
2. Explain a proof of the Pythagorean Theorem using area rearrangement (four congruent right triangles inside a square), articulating why each step in the proof is valid
3. State the converse of the Pythagorean Theorem and explain how it differs from the theorem itself
4. Use the converse to determine whether a triangle with given side lengths is a right triangle
5. Distinguish between the two directions of reasoning: the theorem starts from "right triangle" and concludes "a^2 + b^2 = c^2," while the converse starts from "a^2 + b^2 = c^2" and concludes "right triangle"