Question

14.
ABCD is a parallelogram, and AE and
CF bisect ZA and ZC respectively.
Prove that AE || FC.​

Answer 1

given :abcd is a llgm

ae bisects angale za and cf bisects zc

to prove :ae ll fc

proof:angle cae =angle eab

angle zcf =angle fcd

angle zcf or anlge acf =1/2 of angle acd (1)

angle aez or angle eac =1/2 of angle cae(2)

Angle bac =angle acd (alternate interior angles)(since ab ll cd)

therefore,

1/2 angle acd =1/2 angle cab

angle eac=angle acd (using (1) &(2) ). (3)

therefore, ae ll fc ( since alternate interior angles are equal (3))

hope it helps

Answer 2

Hope it's help you....