Q. 29

# In a parallelogra

Answer :

In a parallelogram ABCD

AB = 10 cm, AD = 6 cm
DC = AB = 10 cm and AD = BC = 6 cm [In a parallelogram opposite sides are equal]
Given that bisector of
A intersects DE at E and BC produced at F.
Draw PF || CD
From the figure, CD || FP and CF || DP
Hence PDCF is a parallelogram. [Since one pair of opposite sides are equal and parallel]
AB || FP and AP || BF
ABFP is also a parallelogram
Consider ΔAPF and ΔABF
APF = ABF [Since opposite angles of a parallelogram are equal]
AF = AF (Common side)
PAF = AFB (Alternate angles)
ΔAPF
ΔABF (By ASA congruence criterion)
AB = AP (CPCT)
AB = AD + DP
= AD + CF [Since DCFP is a parallelogram]
CF = AB – AD
CF = (10 – 6) cm = 4 cm

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