Question

In the figure, ABCD is a parallelogram
and P, Q are the points on diagonal BD
such that DP = BQ. Prove that CPAQ is a
parallelogram.​

Answer 1

Answer:

Step-by-step explanation:

given that DP = QB

in  ΔDPQ  & ΔABQ

⇒DP = QB    (given)

⇒DC = AB    (side of ║gm)

⇒∠PDC = ∠QBA   (alternate )

⇒ΔCDP ≅ ΔABQ    by SAS  criterian

⇒CP = AQ   (cpct)

similarly we can proove that ΔADP ≅ ΔCBQ

⇒AP = CQ

now in ΔAPQ & ΔPQC

⇒AP = CQ

⇒AQ= PC     (PROVED)

⇒PQ = PQ      (COMMN)

ΔAPQ  is similar to ΔCQP CBY SSS

⇒ ∠APQ = ∠PQC    (CPCT)

⇒  AQ ║ PC             (ALTERNATE INT  ANGLE  R  EQUAL )

⇒ ACPQ  IS  A  PARALELLOGRAM

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Answer 2

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