Question

in the adjoining figure ABC is a triangle in which AD is the bisector of angle A if AD transversal BC show that angle ABC is isosceles

Answer 1

Answer:

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Step-by-step explanation:

Given : AD bisects ∠A and is perpendicular to BC.

To prove : ΔABC is isoceles

Proof :

In ΔABD & ΔADC

∠BAD=∠DAC            (∵  D bisects ∠A)

∠ADB=∠ADC

⇒∠ABD=∠ACD

(∵  if two angles in a triangle are equal to two angles in another triangle, then the third angle of both the triangles must also be equal)

⇒∠B=∠C

∴   AB=AC (if two angles are equal then the side opposite to the angles will also be equal)

Hence proved.