prove that a triangle ABC is an isosceles triangle if the altitude AD from A on BC bisects of BC
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Step-by-step explanation:
Given:- ABC is a Δ with AD Altitude which bisects BC
To Prove:- ABC is an isosceles triangle with AB = AC
Proof:-
AS AD bisects BC,
BD = DC
Now In ΔABD and ΔACD,
∠ADB = ∠ ADC (Given)
BD = DC (Given)
AD = AD (Common)
So ΔABD ≅ triangle ΔACD (By SAS)
Then AB = AC
∠B = ∠C
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