BM and CN are perpendicular to a line passing through the vertex A of a triangle ABC. IF L is the mid point of BC. PROVE THAT,LM=LN

Answer 1

Let P be the foot of the perpendicular from L to MN. Since L is the midpoint of BC, P is the midpoint of LM. Then ∆LPM and LPN are right triangles with equal legs. So, their hypotenuses LM and LN are also equal.