Question

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If the altitude from one vertex of a triangle bisects the opposite side ,prove that the triangle is isosceles

Answer 1

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Answer 2

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Let ABC. is a triangle in which AD. is a bisector of angle BAC which meets the. BC. on D , such that BD= CD.

To prove:- Triangle ABC is an isosceles triangle.

Proof:- In triangle BAD. and triangle CAD.

angle BAD. = angle. CAD. . (given )

side. BD. = side CD. (given)

AD. is common.

∆ BAD. is congruence. ∆ CAD

Therefore side AB. = side. AC. or. ∆ ABC is an isosceles triangle.

Hence Proved...

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