Question

triangle ABC and triangle DBC are two isoceles triangle on the same base BC show that angle ABD and angle ACD are equal..

Answer 1

GIVEN---
ABC is isosceles triangle,
AB = AC
DBC is isosceles triangle

TO PROVE---
angle ABD = angle ACD

PROOF---
join AD

In tri. ABD and ACD

AB = AC    (given)
BD = CD    (given)
AD = AD    (common)

tri.ABD = tri.ACD  (SSS)

angle ABD = angle ACD   (cpct)
                                                  HENCE PROVED

Answer 2

Hello mate ☺

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$\bold\red{Solution:}$

AB=AC                  (Given)

It means that ∠ABC=∠ACB   (In triangle, angles opposite to equal sides are equal) .....(1)

BD=DC             (Given)

It means that ∠DBC=∠DCB    (In triangle, angles opposite to equal sides are equal)  ......(2)

Adding (1) and (2), we get

∠ABC+ ∠DBC=∠ACB+∠DCB

⇒∠ABD=∠ACD

I hope, this will help you.☺

Thank you______❤

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