**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:

(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 (