Q18 of 40 Page 8

ABCD is a parallelogram. P is a point on AD such that AP = 1/3 AD and Q is a point on BC such that CQ = 1/3 BC. Prove that AQCP is a parallelogram.

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.


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