Question

ABC is a right angled triangle with AB = AC. Bisector
of Angle A meets BC at D. Prove that BC = 2AD.

Answer 1

ABC right angled at A and AB = AC

angle A = angle B

Sum of angles of a triangle = 180

Angle A+ angle B + angle C = 180

90+ angle B+ angle B = 180

2 angle B = 180-90

Angle B = 45 . …………………………….(1)

also,

AD is the bisector of BAC

So, angle BAD = angle CAD = 90/2 = 45 …………………………..(2)

Angle BAD = angle ABC

So, AD = BD ………………………………(3) .

Similarly angle CAD = angle ACD

So, AD = DC ………………………………..(4)

Adding equation (3) and (4)

We get ,

AD + AD = BD+DC

2AD = BC

Hence proved

Answer 2

first do the first page then continuation is in 2nd page