In a ΔABC, BM and CN are perpendiculars from B and C respectively on any line passing through A.
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.

Solution:

Given that,

In ΔBLM and ΔCLN

∠BML = ∠CNL = 90°

BL = CL         [L is the mid-point of BC]

∠MLB = ∠NLC      [Vertically opposite angle]

∴  ΔBLM = ΔCLN

∴  LM = LN         [corresponding parts of congruent triangles]

 

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