Question

if the diagonals of a parallelogram are equal then show that it is a rectangle ​

Answer 1

Answer:

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

By CPCT

∴ ∠ABC=∠BAD..

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.

Step-by-step explanation:

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