Question

Prove that triangle Abc isosceles if any one of the following holds (1) bisector if angle bac is perpendicular to bc (2) Altitude ad bisects angle bac (3)Altitude be =altitude cf

Answer 1

Step-by-step explanation:

we have drawn an triangle ABC and AD is the altitude)

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.

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