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Question
In the following figure, BL = CM.
Prove that AD is a median of triangle ABC.
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Solution
In ΔDLB and ΔDMC,
BL = CM ...( given )
∠DLB = ∠DMC ...( Both are 90° )
∠BDL = ∠CDM ....( vertically opposite angels )
∴ ΔDLB ≅ ΔDMC ....( AAS congruence criterion )
BD = CD ....( cpct )
Hence, AD is the median of ΔABC.
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