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, 

In ΔABC, 

BM & CN are perpendiculars from B & C

In ∆BLM and ∆CLN

∠BML =∠CNL= 90°

BL=CL 

[L is mid point of BC]

∠MLB=∠NLC 

[vertically opposite angles]

∴ ∆BLM =  ∆CLN

∴ LM = LN 

(corresponding sides of congruent triangles)