Question

prove that for an isosceles triangle the straight line parallel to the base and passing through the vertex is the external bisector of the vertical angle


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Answer 1

Answer:

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

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.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

prove that for an isosceles triangle the straight line parallel to the base and passing through the vertex is the external bisector of the vertical angle