Question

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answer this question​

Answer 1

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