If the bisector of an angle of a triangle also bisects the opposite side then prove that the triangle is isosceles?
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. Proved.
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If the bisector of an angle of a triangle also bisects the opposite side then prove that the triangle is isosceles?
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. Proved.
Hope it help u