Question

# Question 9 (v) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: APCQ is a parallelogram

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, So , AP= CQ  (CPCT) and  AQ=CP Since opposite sides In quadrilateral APCQ are equal to each other, APCQ is a parallelogram.

Suggest corrections