Question

1. In Fig. 11.37, ABCD is a parallelogram. AF and
CE are the bisectors of angle DAB and angle BCD
respectively. In each of the following if the
statement is true, give reasons:
(a) angle DAB = angle BCD
(b) angle FBE = ½ of angle DAB

(d) Angle DCE = ½ of angle DCB
(c) angle DCE = angle CEB
(e) angle FAB = angle CEB

(f) AF parallel to CE​

Answer 1

Answer:

Since ABCD is a parallelogram, AB∥CD  as opposite sides of a parallelogram are parallel.

And CE is the transversal passing through AB and DC.

=>∠DCE=∠CEB  (Alternate Angles)  -- (1)

Also since ABCD is a parallelogram

=>∠A=∠C (Opposite angles of a parallelogram as equal )

As AF and CE are bisectors of these angles respectively,

∠FAB=∠DCE --- (2)

From , 1 and 2

∠FAB=∠CEB 

This means, the corresponding angles formed by lines CE and FA cut by transversal AB are equal

=>AF∥CE

Answer 2

Answer:

I) true because opp angles are equal so half are also equal as bisected

d) true bisected

c) true alternate angles

e) true corresponding angles

f) true alternate and corresponding angles are equal