Prove that angle ABD is congruent to angle ACD?

Solution:

From the figure,AC = AB

We have to prove that ∠ACD congruent to ∠ABD.

In ΔABC

AC = AB (given)

We know that

Angles opposite to the equal sides of an isosceles triangle are equal.

Consider AD as the angular bisector

∠BAD ≅ ∠CAD

AD ≅ AD (Reflexive property)

So we get 

∠B ≅ ∠C (c.p.c.t)

∠ACD ≅ ∠ABD (SAS Postulate)

Therefore, it is proved.

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Prove that angle ABD is congruent to angle ACD?

Summary:

It is proved that angle ABD is congruent to angle ACD.