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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.
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Solution
In B
Given that
In Δ BLM and Δ CLN
`∠`BML = `∠` CNL = 90°
BL = CL [L is the midpoint of BC]
`∠`MLB = `∠`NLC [vertically opposite angle]
∴ ΔBLM = ΔCLN ( A . L . A . S )
∴ LM = LN [Corresponding plats parts of congruent triangles]
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