Question

in the given figure AD is the bisector of angle A of triangle ABC in which ab is equal to AC prove that angles opposite to equal sides are equal​

Answer 1

Proved below.

Step-by-step explanation:

Given:

Here AD is the bisector of angle A of triangle ABC.

Also AB = AC

To prove:

∠ ABD = ∠ ACD

Proof:

Now, in ΔBAD and ΔCAD

AD = AD              [common]

AB = AC              [Given]

∠ BAD = ∠ CAD   [given AD bisects ∠ BAC]

ΔBAD ≅ ΔCAD    [By SAS test of congruence]

∴ ∠ ABD = ∠ ACD      [By CPCT]

Therefore, angles opposite to equal sides are equal​.

Hence Proved.