Question

which statement correctly defines the converse of the pythagorean theorem? a. if (a^{2}+b^{2}>c^{2}), then the triangle is a right triangle. b. if a triangle is a right triangle, then (a^{2}+b^{2}=c^{2}). c. if (a^{2}+b^{2}=c^{2}), then the triangle is a right triangle. d. if (a^{2}+b^{2}<c^{2}), then the triangle is a right triangle. how does understanding the pythagorean theorem and its converse benefit real - world applications? a. by memorizing mathematical formulas b. by calculating probabilities c. by solving problems involving distances and angles d. by analyzing historical events

Explanation:

The Pythagorean Theorem states that in a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. The converse is that if \(a^{2}+b^{2}=c^{2}\) for a triangle, then it is a right - triangle. Also, understanding the Pythagorean Theorem and its converse helps in solving real - world problems related to distances and angles, like in construction, navigation etc.

Answer:

1. C. If \(a^{2}+b^{2}=c^{2}\), then the triangle is a right triangle.
2. C. By solving problems involving distances and angles.