Question

ABCD is a parallelogram. P and Q are the
midpoints of AB and DC. If P and Q are
joined, prove that APQD is a parallelogram.​

Answer 1

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ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively .

Since ABCD is a parallelogram,AB ║ CD  and AB = CD

P and Q are the mid points  of AB and CD

so, QC = 1/CD =1/AB  = PB

ie. QC = PB

Also PB ║ QC and QC = PB then we get, PQ = BC

Therefore  PBCQ is also a parallelogram.