Maths-

General

Easy

Question

# In the given picture, is an isosceles triangle with and AD bisects the exterior angle A. Prove that

Hint:

### find that alternate interior angles are equal then the lines are parallel.

Using condition given conditions find relation between ∠ C and ∠ ADC.

## The correct answer is: Hence proved

### In ABC,

AB = AE (given)

Then ,∠ B = ∠ C (angles opposite to equal sides are equal )

We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

∠ B + ∠ C = ∠ EAC

Substitute ∠B = ∠C we get,

2∠C = ∠ EAC

But 2 ∠ ADC = ∠ EAC (AD is the angular bisector)

2 ∠C = 2 ∠ ADC

∠ C = ∠ ADC

As we know , ∠ C and ∠ ADC are alternate interior angles .

If alternate interior angles are equal then the lines are parallel.

So, AD || BC

Hence proved

We know that in a triangle, the exterior angle is always equal to the sum of the interior opposite angles.

Substitute ∠B = ∠C we get,

As we know , ∠ C and ∠ ADC are alternate interior angles .

If alternate interior angles are equal then the lines are parallel.

Hence proved

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