Question

ABC and DBC are two isosceles triangle on the same base BC show that angle ABD = angle ACD

Answer 1

Given :- ABC and DBC are isosceles triangle.
To prove :- angle ABD = angle ACD.

So,

AB = AC [Sides of an isosceles triangle are equal]

Similarly,

DB = DC

By this,

angle ABC = angle ACB ---- eq.1 [ Angles opposite to equal sides in a triangle are also equal]

Similarly,

angle DBC = angle DCB ---- eq.2

Adding eq.1 and eq.2,

angle ABC + angle DBC = angle ACB + angle DCB

=> angle ABD = angle ACD.

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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