Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.

Answer:EF = BC = a ÐF is a right angle. FD = CA = b triangle EF = BC = a angle F is a right angle. FD = CA = b In triangle DEF, By Pythagoras Theorem, a2 + b2 = c2 the given AB=c= a^2 + b^2 square root Theorefore AB = DE But by construction, BC = EF and CA = FD triangle ABC congruent to DEF (S.S.SWe have given that Δ ABC is similar to Δ CBD and Δ ABC is similar to Δ ACD according to the attached picture.Because of the similarity the corresponding sides are proportional. Then a/c = f/aand b/e = c/b. If we cross multiply, we'll geta² = cf and b² = ceIf we add these equalities together, we'll geta² + b² = c (f + e)From the beginning, we know that c = e+fThen, the final result is:a² + b² = c²