Question:
In Fig. 17.31, ABCD is a parallelogram, CE bisects ∠C and AF bisects ∠A. In each of the following, if the statement is true, give a reason for the same:.png)
(i) ∠A = ∠C
(ii) $\angle F A B=\frac{1}{2} \angle A$
(iii) $\angle D C E=\frac{1}{2} \angle C$
(iv) $\angle C E B=\angle F A B$
(v) CE || AF
Solution:
(i) True, since opposite angles of a parallelogram are equal.
(ii) True, as AF is the bisector of
(iii) True, as CE is the bisector of
(iv) True
From equations (i) and (ii):
(v) True, as corresponding angles are equal (