Q. 83.9( 13 Votes )

# In a &Del

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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