devarshi-dt-logo

Question:

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

Solution:

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 || BC 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.