The diagonals of a parallelogram are equal in length if and only if the parallelogram is a rectangle.
Any angle of a rectangle is 90°.
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Adjacent angles of a parallelogram are supplementary. If the diagonals are the same length, the triangles formed by either diagonal are congruent with the triangles formed by the other diagonal. This means adjacent angles are congruent. Congruent supplementary angles are 90°.
