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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
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Solution
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
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