Question

ABC is right triangle with AB=AC. Bisector of angle A meets BC at the. Proove that BC.​

Answer 1

Answer:

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Step-by-step explanation:

B

D

90

A C

Here in triangle , ABC right angled at A and AB = AC

Hence angle A = angle B

We have , 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 eqn (3) and (4)

We get , AD + AD = BD+DC

2AD = BC

HENCE PROVED