Question

ABCD is a parallelogram in which bisectors of angle A and angle C meet the diagonal BD at P and Q respectively. prove PCQA is a parallelogram.​

Answer 1

Answer:

PCQA is a parallelogram

Step-by-step explanation:

Δ APB & ΔDCQ

∠BAP = ∠DCQ  =  ( Bisector of Angle A & C)

∠ABP = ∠CDQ  ( BD cuts parallel lines)

AB = CD ( opposite sides of parallelogram)

Δ APB ≅ ΔDCQ

=> AP = CQ

Similarly

ΔADQ ≅ ΔCBP

=> AQ = CP

AP = CQ

AQ = CP

=> PCQA is a parallelogram

Answer 2

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