Question

In fig.17.31,ABCD is a parallelogram,CE bisects angle C and AF bisects angle A.In each of the following,if the statement is true,give a reason for the same:(​

Answer 1

Answer:

In fig.17.31,ABCD is a parallelogram,CE bisects angle C and AF bisects angle A.In each of the following,if the statement is true,give a reason for the same:(

Answer 2

Step-by-step explanation:

(i) ∠A = ∠C True, Since ∠A =∠C = 55° [opposite angles are equal in a parallelogram]

(ii) ∠FAB = ½ ∠A True, Since AF is the angle bisector of ∠A.

(iii) ∠DCE= ½ ∠C True, Since CE is the angle bisector of angle ∠C.

(iv) ∠CEB= ∠FAB True, Since ∠DCE = ∠FAB (opposite angles are equal in a parallelogram). ∠CEB = ∠DCE (alternate angles) ½ ∠C = ½ ∠A [AF and CE are angle bisectors]

(v) CE || AF True, since one pair of opposite angles are equal, therefore quad. AEFC is a parallelogram.