Question

12. In the adjoining figure, AABC is an isosceles triangle in which
AB = AC and AD is the bisector of ZA.
Prove that:
AADB AADC
B
D C
(ii) ZB = ZC
(iii) BD = DC
(iv) AD IBC
A in written form
​

Answer 1

Step-by-step explanation:

Method 1:

When AD is the angle bisector of <BAC

ABC is an isosceles triangle in which AB = AC and AD is the bisector of <BAC.

In triangles ABD and ACD

<B = <C

AB = AC

AD is common.

Therefore triangles ABD and ACD are congruent, and so

<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.

QED.

Method 2:

When AD is the bisector of BC

ABC is an isosceles triangle in which AB = AC and AD is the bisector of BC.

In triangles ABD and ACD

<B = <C

AB = AC

BD = CD.

Therefore triangles ABD and ACD are congruent, and so

<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.

QED.

Hence proof