Question

ABC and DBC are two isosceles triangles the same basic BC. show that ∆ABD=∆ACD​

Answer 1

$\sf\huge\bold{Answer:}$

Given: 

ABC and DBC are isosceles triangles

To Prove: 

∠ABD = ∠ACD

Construction :

Join point A and point B.

Solution :

In △DAB and △DAC,

AB = AC (Given)

BD = CD (Given)

AD = AD (Common side)

∴ △ ABD ≅ △ ACD

$\sf (By SSS congruence \: rule)$

$\bf\purple {∴ ∠ABD = ∠ACD}$ (By CPCT)

Hence proved !