Q. 14.1( 42 Votes )

# In figure 5.22, ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove APCQ is a parallelogram.

Answer :

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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