Question

# 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) ∴ΔAPD≅ΔCQB (using SAS congruence rule) As we have proved that triangle APD is congruent to triangle  CQB, Hence, AP= CQ (CPCT)

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