Question

18. Prove that AABC will be an isosceles triangle in which AB = AC if and only if:
(1)
Median AD is I on BC
(ii) Bisector of ZBAC is I on BC
111
Altitude AD, bisects ZBAC.
(iv)
Altitude BE=Altitude CF
(v)
Median BE=Median CF​

Answer 1

Answer:

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Answer

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(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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Answer 2

Answer:

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