Question

If the Diagonals of a Parallelogram are equal ,then show that it is rectangle.​

Answer 1

Step-by-step explanation:

Ref.Image

□ ABCD is a parallelogram

consider Δ ACD and Δ ABD

AC = BD     (given)

AB = DC     (opposite sides of parallelogram)

AD = AD     (common side)

∴Δ ACD ≅Δ ABD     (sss test of congruence)

∠ BAD = ∠ CDA      (cpct)

∠BAD+∠CDA=180°     [Adjacent angles of parallelogram are supplementary]

so, ∠BAD and ∠CDA are right angles as they are congruent and supplementary.

Therefor, ABCD is a rectangle since a  

parallelogram with one right interior angle is a rectangle.