Mathematics
In the following figure, BL = CM. Prove that AD is a median of triangle ABC.
Triangles
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Answer
In △ BLD and △ CMD,
⇒ BL = CM (Given)
⇒ ∠BLD = ∠CMD (Both equal to 90°)
⇒ ∠BDL = ∠CDM (Vertically opposite angles are equal)
∴ ∆ BLD ≅ ∆ CMD (By A.A.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ BD = CD.
Thus, we can say that :
AD bisects BC in two equal halves.
Hence, proved that AD is a median of triangle ABC.
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