In Fig. 17.31, ABCD is a parallelogram, CE bisects ∠C andAF bisects ∠A. In each of the following, if the statement is true, give a reason for the same.

Question

In Fig. 17.31, ABCD is a parallelogram, CE bisects &#x2220; C and AF bisects &#x2220; A . In each of the following, if the statement is true, give a reason for the same.

Philoid · Accepted Answer

(i) ∠A = ∠C

True,

∠C =∠A = 55° [In a parallelogram opposite angles are equal]

(ii) ∠FAB=∠A

True,

AF is the angle bisectoe of angle A

(iii) ∠DCE=∠C

True,

CE is the angle bisectoe of angle A

(iv) ∠CEB= ∠FAB

True,

∠C = ∠A [In a parallelogram opposite angles are equal]

[AF and CE are angle bisectors]

(v) CE || AF

True, Since one pair of opposite angles are equal, therefore Quad AEFC is aparallelogram.