Question

If the diagonals of parallelogram are equal then it will we a rectangle.

Answer 1

Given parallelogram ABCD, AC$=$BD

Proof:- In $\Delta ABC$ & $\Delta ABD$

$AB=AB$(common)

$AC=BD$ (given)

$BC=AD$(opposite sides of parallelogram)

$\therefore ABC\cong BAD$(congruence)

also $\angle ABC+\angle BAD={180}^o$ (co-interior angle)

$\angle ABC+\angle ABC={180}^o$ $(\because \angle ABC=\angle BAD)$

$\Rightarrow 2\angle ABC={180}^o$

$\angle ABC={90}^o$

Hence it is rectangle.