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Question

Prove that in an isosceles triangle the perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

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Solution

Let ABC be an isosceles triangle such that AB=AC.
Let AD be the bisector of A.
To prove:- BD=DC
Proof:-
In ABD&ACD
AB=AC(ABC is an isosceles triangle)
BAD=CAD(AD is the bisector of A)
AD=AD(Common)
By S.A.S.-
ABDACD
By corresponding parts of congruent triangles-
BD=DC
Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.

967165_1041364_ans_b320021d10a943b8a4b14dd0a6b67a15.jpeg

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