Question

in a triangle ABC bisector of angle BAC meets opposite side BC at a point D if BD =CD prove triangle ABC is isosceless

Answer 1

In Triangle ABD and ACD
AD = AD (common)
_/BAD = _/CAD (AD bisects A)
BD = CD  (given)
By ASA rule,

TRI. ABD IS CONGRUENT TO TRI.ACD

THEN ANGLE ABD = ANGLE ACD 

HENCE PROVED