Question

In Fig. 9.38, AE bisects ∠CAD and ∠B =∠C. Prove that AE||BC.

Answer 1

Corresponding angles are equal so we can say that AE║BC.

Step-by-step explanation:

Given:

$\angle B = \angle C$

AE bisects ∠CAD

So we can say that;

$\angle DAE =\angle CAE$

We need to prove that AE║BC.

Solution:

Now we know that;

By Exterior angle property

"Sum of the opposite interior angles are equal to the exterior angle."

$\angle B + \angle C = \angle CAD$ ⇒ (Exterior Angle property)

But We know that;

$\angle CAD = \angle DAE +\angle CAE$

But $\angle DAE =\angle CAE$  (given)

$\angle B + \angle C = \angle DAE + \angle DAE$

Also $\angle B = \angle C$ (given)

$\angle B + \angle B = \angle DAE + \angle DAE\\\\2\angle B = 2\angle DAE$

Dividing both side by 2 we get;

$\frac{2\angle B}{2} =\frac{ 2\angle DAE}{2}\\\\\angle B= \angle DAE$

Hence corresponding angles are equal so we can say that AE║BC.

Hence Proved.