Question

1. which statement correctly defines the converse of the pythagorean theorem? a. if a² + b² > c², then the triangle is a right triangle. b. if a triangle is a right triangle, then a² + b² = c². c. if a² + b² < c², then the triangle is a right triangle. d. if a² + b² = c², then the triangle is a right triangle.

Explanation:

The Pythagorean Theorem states that for a right - triangle, $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs and $c$ is the hypotenuse. The converse starts with the equation $a^{2}+b^{2}=c^{2}$ and concludes that the triangle is a right - triangle.

Answer:

D. If $a^{2}+b^{2}=c^{2}$, then the triangle is a right triangle.