Question

In the adjoining figure, ABC is a triangle in which AD is the bisector of <A.
If AD perpendicular BC, show that triangle ABC is isosceles.​

Answer 1

Answer:

In triangle ABD and ACD

Angle BAD = Angle CAD [ As AD is bisector]

AD = AD [Common side]

Angle ADB = Angle ADC = 90degree [AD is perpendiculatr to BC]

Therefore, triangle ABC is congruent to triangle ACD by SAS congruence rule.

Now, angle B = angle C by CPCT.

Hence, AB=AC as the angles opposite to them are equal.

Therefore, triangle ABC is an isosceles triangle.

Hope this will help.