Question

Hi Friends,

Prove that ∆ ABC is isosceles if median AD is perpendicular to BC.

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Class - 9th
Chapter - Triangle

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Answer 1

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Solution :-

Given :- A ∆ABC , in which median AD is ⊥to BC.

To prove :- ∆ABC is Isosceles.

Proof :- In ∆ ABD and ∆ ACD ,

We have ,

⇒BD = DC(Given)

⇒∠ ADB = ∠ADC ( Each = 90°)

⇒AD = AD ( Common side)

⇒∆ ABD ≌ ∆ ACD ( By SAS )

⇒AB = AC ( ∵ C.P.C.T )

∴ ∆ ABC is an isosceles triangles. Proved.

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