Question

the given Δ ABC, AB = AC, D is a point inside the triangle such that BD = DC. Prove that ∠= ∠. Justify your answer using appropriate axiom

Answer 1

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Step-by-step explanation:

Given=> AB=AC

BD=DC

Construction => Join AD

To prove that => angle ABD = angle ACD

Proof=> In triangle ADB & ADC

AD=AD [Common]

BD=CD [Given]

AB=AC [Given] Triangle ADB is congruent to Triangle ADC.

Therefore,

Angle ABD = Angle ACD

Answer 2

Here,

AB = AC

 ABC = ACB (Angles opp. to equal sides are equal)

Also, BD = DC

DBC = DCB (Angles opp. to equal sides are equal)

Subtracting,

ABC - DBC = ACB - DCB

 ABD = ACD

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