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Question

In the given figure, AP is bisector of A and CQ is bisector of C of parallelogram ABCD.
Prove that APCQ is a parallelogram
195067.jpg

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Solution

Consider ADP & QBC
D=B (Opposite side of parallelogram.)
DA=BC (Opposite side of parallelogram.)
x=x [bisector of opposite angle.]
By ASA congruence rule. [ADPQBP]
then by CPCT, DP=QB(1)
x=x [bisector of opposite angle.]
ADPQBP [by ASA]
AB=DC [opposite side of a parallelogram.]
AQ+QB=DP+PC [QB=DP from 1]
AQ=PC(2)
Hence distance between AP and QC are equal at all place hence proved APQC(3)
AQCP is parallelogram.

1039337_195067_ans_7c50974bb6c54315bdc2de5b4d3e219f.png

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