Parallelograms Theorem 3

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Statement

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

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)

AC = AC (common side)

(corresponding parts of corresponding triangles)

Since these are alternate angles, AD||BC.

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

ABCD is a parallelogram.