Question

In a triangle ABC, the bisector AD of angle A is perpendicular to the side BC. Prove that ∆ABD = ∆ ACD. ​

Answer 1

In triangle ABD and triangle ACD,

angle ADB = angle ADC (AD perpendicular to BC)

AD=AC (common side)

BD=CD (half of the base)

By using 'SAS' criteria

triangle ABD is congruent to triangle ACD.

HENCE PROVED.