Q19 of 97 Page 187

In the adjoining figure, AD is a median of ∆ABC. If BL and CM are drawn perpendiculars on AD and AD produced, prove that BL=CM

Given: BC = DC and BL ⊥ AD and DM ⊥ CM


To prove: BL=CM


Proof:


In ∆BLD and ∆CMD,


∠BLD = ∠CMD = 90° … given


∠BLD = ∠MDC … vertically opposite angles


BD = DC … given


Thus by AAS property of congruence,


∆BLD ≅ ∆CMD


Hence, we know that, corresponding parts of the congruent triangles are equal


∴ BL = CM


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