Proof this : The angles and the isosceles angles of an angle are perpendicular to each other.
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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.-
△ABD≅△ACD
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.
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