Question

The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that:  ΔAMC≅ ΔANB

Answer 1

In ΔABC, AB = AC. m and N are points on
AB and AC such that BM = CN
BN and CM are joined

Consider the triangles AMC and ANB
AC = AB         [ given ] 
LA = LA          [ common ]
AM = AN        [ from ( 3 ) ]
∴ By Side-Angel-Side Criterion of congruence, we have ΔAMC≅ ΔANB