Question

Abcd is right triangle in which angle A=90° and ab=ac show that ad bisects bc and ad bisects anlge a​

Answer 1

Given: ∆ABC with ∠A = 90° and D is mid-point of BC. (It must be mid-point, else question remains incomplete.)

Also, AB = AC

To show: CD = DB and ∠CAD = ∠BAD

Proof:

As D is mid-point of BC,

CD = DB ...(1)

In ∆ABC,

As AC = AB, (Given)

=> ∠C = ∠B ...(2)

(Angles opposite to equal sides)

Now, in ∆ACD & ∆ABD,

CD = DB [By (1)]

∠C = ∠B [By (2)]

AC = AB [Given]

So, ∆ACD ≅ ∆ABD (SAS congruency)

=> ∠CAD = ∠BAD (CPCT)