Question

$\text{If the diagonals of a parallelogram are of equal lengths, the parallelogram is arectangle. Prove it.}$

Answer 1

$\text{Given :}||\text{gm ABCD in which}AC=BD\text{To Prove : ABCD is rectangle.}\text{Proof : In}\Delta ABCand\Delta ABDAB=AB\text{(Common)}AC=BD\text{(Given)}BC=AD\text{(opposite sides of}||gm)\therefore \Delta ABC\cong \Delta ABD\text{(S.S.S. Rule)}\therefore \angle A=\angle BButAD||BC(\therefore \text{opp. sides of}||gmare||)\therefore \angle A+\angle B={180}^{\circ }\therefore \angle A=\angle B={90}^{\circ }\text{Similarly}\angle D=\angle C={90}^{\circ }\text{Hence ABCD is a rectangle.}.$