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Question 9 (ii)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
AP = CQ


Solution

In ΔAPD and ΔCQB,
ADP=CBQ
(Alternate interior angles)

AD =CB (Opposite sides of parallelogram ABCD)
DP=BQ (Given)

ΔAPDΔCQB
(using SAS congruence rule)

As we have proved that triangle APD is congruent to triangle  CQB,
Hence, AP= CQ (CPCT)

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