Question

In ∆ ABC , BM & CN are perpendiculars from B and C respectively on any line passing through A . If L is the mid-point of BC , prove that ML = NL .​

Answer 1

In ∆BLM and ∆CLN

∠BML = ∠CNL = 90 degrees

Therefore, BL = CL

∠MLB = ∠NLC

So ∆BLM and ∆CLN are congruent

LM = LN (corresponding parts of congruent triangles)