Question 9 (iv) In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that: AQ = CP
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Solution
In ΔAQB≅ΔCPD, ∠ABQ=∠CDP (Alternate interior angles for AB||CD) AB=CD (Opposite sides of parallelogram ABCD) BQ=DP( Given) ΔAQB≅ΔCPD (Using SAS congruence rule) As ΔAQB≅ΔCPD, ⇒AQ=CP (CPCT)