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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) AM = AN (ii) ΔAMC ≅ ΔANB
Solution
In ΔABC, AB = AC. m and N are points on
AB and AC such that BM = CN
BN and CM are joined
(i) In ΔAMC and ΔANB
AB = AC ...[ Given ] ...(1)
BM = CN ....[ Given ] ...(2)
Subtracting (2) from (1), we have
AB - BM = AC - CN
⇒ AM = AN ...(3)
(ii) Consider the triangles AMC and ANB
AC = AB ...[ given ]
∠AMC = ∠ANB ...[ common 90° ]
AM = AN ....[ from ( 3 ) ]
∴ By the Side-Angel-Side Criterion of congruence, we have ΔAMC ≅ ΔANB
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