Question

Prove that If two diagonals of a parallelogram are equal, it is a rectangle.

Answer 1

Given:

ABCD is a parallelogram in which AC=BD.

To prove:

Parallelogram ABCD is a rectangle.

Proof:

In triangles ABC and DBC,

AB=DC (opposite sides of parallelogram)

BC=BC (common side)

AC=BD (given)

But these angles are consecutive interior angles on the same side of transversal BC and AB||DC.

By definition of rectangle, parallelogram ABCD is a rectangle.

Hence the theorem is proved.