Question

In triangle ABC, AB = AC, AD is the bisector of angle A prove that
i) D is the mid pt. of BC ii) AD bisector of BC​

Answer 1

Step-by-step explanation:

1) As AD is the bisectoe of angle A

therefore,

angle BAD = angle DAC

hence,

BD=DC (sides opposite to equal angles are equal)..........(i)

Now,

BD+DC=BC

BD+BD=BC (from (i))

2BD=BC

therefore,

D is the midpoint of BC.......(A)

And AD is the bisector of BC..........(B)

from,

(A) and (B)

hence proved......

Hope this solves your requirement....

Answer 2

Answer:

I want to prove an additional answer which is asked many a times in exams

that is to prove that AD is perpendicular bisector of BC

in that case <BDA =<CDA(cpct)

also,

<BDA+<CDA=180°(linear pair)

therefore,

2<BDA= 180°

or, <BDA=90°

also , we have proved

BD=DC

thus AD is Perpendicular bisector of BC

Step-by-step explanation:

hope it helps you