Question

Here's a Maths Question !

Prove that the line segment joining midpoints of non - parallel sides of a trapezium is parallel to parallel sides.

Answer 1

Question :

Prove that the line segment joining midpoints of non - parallel sides of a trapezium is parallel to parallel sides.

Solution :

Refer to the above attachment !!

Answer 2

Step-by-step explanation:

ABCD is a trapezium in P and Q are mid-points of non-parallel sides AD and BC.

Prove: PQ || AB.

Construction: Join DQ and produce to meet AB produced at R.

In ΔCDQ and ΔBRQ,

⇒ CQ = BQ

⇒ ∠CQD = ∠BQR [Vertically Opposite angles]

⇒ ∠CDQ = ∠BRQ [Alternate angles]

∴ ΔCDQ ≅ ΔBRQ

We know that Corresponding parts of congruent triangles are equal.

∴ DQ = QR

∴ DC = BR

In ΔADR, P is the mid-point of AD and Q is the mid-point of RD.Therefore, by the converse of mid-point theorem, we have

∴ PQ || AB

Hope it helps!