Answer :

We have


To show that, MN BC.


Given that, B = C and BM = CN.


So, AB = AC [sides opposite to equal angles (B = C) are equal]


Subtract BM from both sides, we get


AB – BM = AC – BM


AB – BM = AC – CN


AM = AN


AMN = ANM


[angles opposite to equal sides (AM = AN) are equal] …(i)


We know in ∆ABC,


A + B + C = 180° [ sum of angles of a triangle is 180°] …(ii)


And in ∆AMN,


A + AMN + ANM = 180° [ sum of angles of a triangle is 180°] …(iii)


Comparing equations (ii) and (iii), we get


A + B + C = A + AMN + ANM


B + C = AMN + ANM


2B = 2AMN [ from equation (i), and also B = C]


B = AMN


Thus, MN BC since the corresponding angles, AMN = B.


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