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If from any point on the base of an isosceles triangle, perpendicular are drawn to the equal sides, prove that the sum of these perpendiculars is equal to the altitude on either of the equal sides

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Maths

The Triangle and Its Properties

Isosceles and Equilateral Triangles

Prove that in an isosceles ...

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Asked on December 26, 2019 by

Tanisha Gersappa

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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ANSWER

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.