Question

If the diagnonals of a parallelogram are equal then show that it is rectangle​

Answer 1

Given: In parallelogram ABCD, AC=BD

To prove : Parallelogram ABCD is rectangle.

Proof : in △ACB and △BDA

AC=BD ∣ Given

AB=BA ∣ Common

BC=AD ∣ Opposite sides of the parallelogram ABCD

△ACB ≅△BDA∣SSS Rule

∴∠ABC=∠BAD...(1) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

∴∠BAD+∠ABC=180 ...(2) _ Sum of consecutive interior angles on the same side of the transversal is 180

From (1) and (2) ,

∠BAD=∠ABC=90

∴∠A=90 and ∠C=90

Parallelogram ABCD is a rectangle.