Question

Prove that A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel.

Answer 1

Given:

ABCD is a quadrilateral in which AB||CD and AB=CD.

To prove:

ABCD is a parallelogram.

Construction:

Join AC.

Proof:

In triangles ABC and ADC,

AB=CD (given)

Since these are alternate angles, AD||BC.

Thus in the quadrilateral ABCD, AB||CD and AD||BC

ABCD is a parallelogram.