Question

In figure angle BMN = angle CMN and AN bisects angle BAC. Prove that triangle ABM congruent to triangle ACM

Answer 1

we have angle BMN equal to angle CMN . so
180-angle BMN =180-angleCMN
Angle BMA=angle CMA
and as we know angle CAM =angle MAB
in triangle AMB and triangle AMC we have
AM =AM
Angle CAM =angle BAM
angle BMA=angle CMA
so these triangle are congruent