Question

Show that in a trapezium the line joining the midpoint of non-parallel sides is parallel to the parallel sides.

Answer 1

Let ABCD be a trapezium such that AD || BC and P and Q are the midpoints of AB and CD respectively.

Construction: Produce BA and CD to meet at S.

We need to prove that PQ || AD || BC

In ΔSBC, AD || BC

Applying Basic Proportionality Theorem, we get:

⇒ AD || PQ (Converse of Basic Proportionality Theorem)

Since AD || BC, PQ || BC

Hence,