Question

in the adjacent figure it is the bisector of angle A if angle ADC is equal to 90 degree prove that angle ABC is isosceles triangle

Answer 1

after doing congruent you can proof it

Answer 2

Answer: If AD is bisector of angle A then, ∠BAD=∠CAD

In ΔBAD and ΔCAD

∠BAD=∠CAD                     (proved above)

AD=AD                               (common)  

∠ADB=∠ADC=90°             (Given, each 90°)

so, ΔBAD ≅ ΔCAD             (by ASA congurency rule)

so, AB=AC                    (by cpct)

so, ABC is an isoceles rianle as it has two sides equal