Question

Prove that a parallelogram with 2 congruent diagonals is a rectangle.

Answer 1

Consider it as though the diagonals are the hypotenuses of two right triangles and if the hypotenuses are equal, then the legs must be equal too.

Answer 2

Prove using congrunecy of triangles in a parallelogram diagonals bisect each other take two adjacent triangles and since diagonals are equal the two triangles are congruent hence you get that its a rhombus as sides are equal to prove angle is 90 just take the two parallel sides and apply properties to get it. Its not too hard i suppose.