The figure below is used to prove the converse of the Pythagorean theorem. In the figure, .

Question

A right triangle A-B-C with base a units, height b units, and hypotonus c units has squares on each side of the triangle.

Which statement describes the converse of the Pythagorean theorem?

A.
If a triangle is a right triangle, then the product of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

B.
If the sum of the squares of the lengths of two sides of a triangle equals the square of the length of the third side, then the triangle is a right triangle.

C.
If a triangle is a right triangle, then the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

D.
If the product of the squares of the lengths of two sides of a triangle equals the square of the length of the third side, then the triangle is a right triangle.

Answer 1

B. If the sum of the squares of the lengths of two sides of a triangle equals the square of the length of the third side, then the triangle is a right triangle.