Use the figures to complete the statements proving the converse of the Pythagorean theorem. Drag and drop a phrase, value, or equation into the box to correctly complete the proof.

To prove the converse of the Pythagorean theorem, we must show that if △ABC has sides of a, b, and c such that a² + b² = c² , then △ABC is a right triangle.

Define △DEF so that it is a right triangle with sides a, b, and hypotenuse x. By the Pythagorean theorem, a² + b² = x² .

Since a² + b² = c² and a² + b² = x², it must be true that c² = x². Since sides of triangles are positive, then we can conclude that Response area. Thus, the two triangles have congruent sides and are congruent.

Finally, if △ABC is congruent to a right triangle, then it must also be a right triangle.

Two right triangles with points labeled in capital letters and sides labeled in lower case letters.