Question

Prove that triange ABC is isosceles if any one of the following holds :- 1) Bisector of angle BAC is perpendicular to BC 2) Altitude AD bisects angle BAC 3) Altitude BE = Altitude CF PLZZZZ ANSWERRR FASTTTTTTT

Answer 1

(1)Given : A triangle ABC  in which BD = DC

to prove : AB = AC or ABC is an isosceles triangle .

 

 Proof:

 

In triangle ABD and triangle ADC

AD = AD ( common)

∠ADB = ∠ADC (90° each)

BD = DC (given)

so Δ ABD ≡ ΔACD( by RHS)

So AB = AC (by cpct)

∴ Δ ABC is an isosceles triangle

(2)

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