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Step-by-step explanation:
Given- ABCD is a parallelogram
DP=PQ
To Prove- APCQ is a parallelogram
Proof- ABCD is parallelogram
In ΔAPD and ΔBQC,
AD=BC. (its a parallelogram)
DP=BQ. (given)
angle ADP=angle CBQ. (alternate
angles)
Therefore by SAS criteria, ΔAPD =~ΔCBQ
ΔBQA=~ΔDPC
THEREFORE, by CPCT
AP=QC
PC=AQ
Therefore, opposite sides are parallel and equal.
Therefore, APCQ is a parallelogram.
HENCE, PROVED
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