Question

in a triangle ABC ad is the bisector of angle BAC and also bisect the sides BC to prove that an ABC is an isosceles triangle

Answer 1

In triangle ADB and triangle ADC
angle DAB =angle DAC---AD is angle bisecter
segBD=segDC---AD bisects BC
segAD=segAD---common side
therefore
triangleADB=triangleADC----SAS test
therefore segAB=segAC---C.S.C.T
since two sides of a triangle are congruent the following triangle is a isosceles triangle