Question

1)Prove that in ∆ ABC, if bisector of ∠ BAC is perpendicular to side BC, then ∆ ABC is an
isosceles triangle.​

Answer 1

Let the bisector of angle BAC and perpendicular to side BC is D

In triangle ABD and ACD

Angle BAD = Angle CAD

[angle BAC is bisector,given]

angle ADB = Angle ADC

[ Both are prependicular , given]

AD = AD [ Common ]

therefore , ∆ ABD congruent ∆ ACD

→ AB = AC [ BY, CPCT ]

therefore ABC is isosceles