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

The converse of the Pythagorean theorem states that if △ABC has sides of a, b, and c such that a² + b² = c² , then​△ABC​ is a Response area.

To prove this, consider the right triangle ​△DEF​ with sides a, b, and x. By the Pythagorean theorem, we know that for this triangle, a² + b² = x².

Since ​​a² + b² = c² and a² + b² = x²​​, it must be true that c² = x² . Because sides of triangles are positive, then we can conclude that c = x. 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.