Question

The following figure has 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: (i) BN = CM (ii) ΔBMC ≅ ΔCNB   

Answer 1

In ΔABC, AB = AC. m and N are points on

AB and AC such that BM = CN

BN and CM are joined

(i) The corresponding parts of the congruent triangles are congruent.

∴ CM = BN         ...[ c.p.c.t ] ...(1)

(ii) Consider the triangles ΔBMC and ΔCNB

BM = CN      ...[Given] 

BC = BC       ...[Common]

CM = BN      ...[From (1)]

∴ By Side-Side-Side criterion of congruence, we have ΔBMC ≅ ΔCNB