Question

ABC AND DEF TWO ISOSCELES TRIANGLEON THE SAME BASE BC SHOW THAT ANGLE ABD = ACD​

Answer 1

Given:

ABC and DBC are two isosceles triangles.

To Prove:

∠ABD = ∠ACD

Proof:

In ΔABC,

AB =AC. (given)

∠ACB= ∠ABC......(1)

[Since angles opposite to equal sides of a triangle are equal]

In ∆ DBC,

DB=DC (given)

∠DCB = ∠DBC......(2)

[Since angles opposite to equal sides of a triangle are equal]

On adding eq 1 & 2 , We get

∠ACB+ ∠DCB= ∠ABC+ ∠DBC

∠ACD= ∠ABD

Hence, ∠ACD = ∠ABD

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Hope this will help you....