ABCD is a p

To Prove: AQCP is a parallelogram

Given: ABCD is a parallelogram. AP = 1/3 AD and CQ = 1/3 BC.

Concept Used:

Opposite sides of a parallelogram are equal and parallel.

Diagram:

Proof:

Then, PQ││BC and PQ = 1/2 BC…………….(i)

In ∆APQ, D and E are midpoints of AP and AQ resp.

∴DE││PQ, DE = 1/2 PQ………….(ii)

From (i) and(ii)

DE = 1/2 PQ = 1/4 BC

DE = 1/4 BC

Hence, Proved.