Question

If the diagonals of a parallelogram are equal, prove that it is rectangle.

Answer 1

R.E.F image

$In△$ ABC &$△DCB$

AB=CD

BC=CB

AC=BD

$\therefore$ $△ABC\cong △DCB$

Hence, $[\angle B=\angle c]$

But

$\angle B+\angle C={180}^{\circ }$

$Thus,[\angle B=\angle C={90}^{\circ }]$

$Hence,[\angle A=\angle D={90}^{\circ }]$

Thus, ABCD is a rectangle