Question

If the diagonals of a parallelogram are equal, then show that it is a rectangular.

Answer 1

Ref.Image

$\square$ ABCD is a parallelogram

consider $\Delta$ ACD and $\Delta$ ABD

AC = BD .... (given)

AB = DC .... (opposite sides of parallelogram)

AD = AD .... (common side)

$\therefore \Delta$ ACD $\cong \Delta$ ABD (sss test of congruence)

$\angle$ BAD = $\angle$ CDA .... (cpct)

$\angle BAD+\angle CDA={180}^{\circ }.$ [Adjacent angles of parallelogram are supplementary]

so $\angle$ BAD and $\angle$ CDA are right angles as they are congruent and supplementary.

Therefor, $\square$ ABCD is a rectangle since a

parallelogram with one right interior angle is a rectangle.