Question

In the figure given below. ABC is an isosceles triangle in which AB + Ac and
AD, is the bisector of LBAC.
Prove that / ABC = LACB
​

Answer 1

Answer:

ABC is an isosceles triangle in which AB=AC and AD is the bisector. How do I prove that ADB=90 degrees?

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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.

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