Question

in the adjoining figure ABCD is a parallelogram such that AB is equal to 10 cm and BC is equal to 6 cm. AEbisects Angle A find the length CF​

Answer 1

Step-by-step explanation:

Very easy

Given AB = 10 cm, AD = 6 cm ⇒ DC = AB = 10 cm and AD = BC = 6 cm 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. 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 = (10 – 6) cm = 4 cm

Hope this helps.......