Question

In a ΔABC, BM and 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

Given that, 

In ΔBLM and ΔCLN 

∠BML = ∠CNL = 90° 

BL = CL [L is the mid-point of BC] 

∠MLB = ∠NLC [Vertically opposite angle]

By ASA criterion: 

ΔBLM ≅ ΔCLN 

So, LM = LN [By CPCT]