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.

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To prove the converse of the Pythagorean theorem, we can define a right triangle, Response area, with sides a, b, and x. Then, we will show that if ​△ABC​ is a triangle with sides a, b, and c where a² + b² = c², then it is congruent to △DEF and therefore a right triangle.

By the Pythagorean theorem, because ​△DEF​ is a right triangle, a² + b² = x².

If ​​a² + b² = x² and a² + b² = c² ​​, then c² = x². Further, since sides of triangles are positive, then we can conclude that ​c = x​. Thus, the two triangles have congruent sides and are congruent.

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.