Question

Malcolm wants to prove the converse of the Pythagorean Theorem. He takes the following steps.

He draws a triangle with side lengths and , such that .
Then, he draws a second triangle with sides lengths and , such that sides and form a 90-degree angle.
Finally, he uses the Pythagorean Theorem to find the length of , the third side of the second triangle. He finds that .

What can Malcolm conclude from these steps?

Answer 1

Malcolm can conclude that if the side lengths and satisfy the condition , then the triangle formed by these side lengths is a right triangle, with the side lengths and forming a 90-degree angle. This proves the converse of the Pythagorean Theorem, which states that if a triangle is a right triangle with side lengths and , then the side lengths satisfy the condition .