Question

In a ∆ABC, M and N are points on the sides AB and AC respectively such that BM = CN. If ∠B = ∠C then show that MN || BC.

Answer 1

In ∆ABC, M and N are points on the sides AB and AC respectively such that BM = CN and if ∠B = ∠C.

We know that, sides opposite to equal angles are equal.

AB = AC

BM = CN ( given)

AB – BM = AC – CN

=> AM = An

From ∆ABC

AM/MB = AN/NC

Therefore, MN ||BN