Question

If the diagonals of a parallelogram are equal, then show that it is a 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...(i) CPCT

Again AD ∥ ∣ Opposite sides of parallelogram ABCD

AD ∥BC and the traversal AB intersects them.

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

 

From (i) and (ii) ,

∠BAD=∠ABC=90  

 

∴∠A=90   and ∠C=90  

 

Parallelogram ABCD is a rectangle.