In a Δ ABC, 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.

Question

In a &#x394; ABC, 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.

Philoid · Accepted Answer

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)

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.