If diagonal of parallelogram are equal show that it is rectangle .

1.	If diagonal of parallelogram are equal show that it is rectangle .
Answer» Given that the diagonals AC and BD of parallelogram ABCD are congruent.Consider triangles ABD and ACD.AC = BD [Given]AB = DC [opposite sides of a parallelogram]AD = AD [Common side]∴ ΔABD ≅ ΔDCA [SSS congruence criterion]∠BAD = ∠CDA [CPCT]∠BAD + ∠CDA = 180° [Adjacent angles of a parallelogram are supplementary.]So, ∠BAD and ∠CDA are right angles as they are congruent and supplementary. Therefore, parallelogram ABCD is a rectangle since a parallelogram with one right interior angle is a rectangle.

Discussion