Given AB ∥ to DC and AB = DC as ABCD is ∥gram.
⇒ AP ∥CQ (parts of ∥ sides are ∥) & 1/2 AB = 1/2 DC
⇒ AP = QC (P and Q are midpoint of AB and DC respectively)
⇒ AP = PB and DQ = QC
Hence APCQ is a parallelogram as the pair of opposite sides is = and ∥.
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