Q. 2

# In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.

Given, AB = 10 cm, AD = 6 cm
DC = AB = 10 cm and AD = BC = 6 cm
Given, bisector of
A intersects DE at E and BC produced at F.
Now, drawing PF || CD.
From the figure, CD || FP and CF || DP
PDCF is a parallelogram.
And , AB || FP and AP || BF
ABFP is also a parallelogram
In ΔAPF and ΔABF
APF = ABF (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
= (10 – 6) cm = 4 cm

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