Mathematics
In the adjoining figure, AD is median of △ABC, BM and CN are perpendiculars drawn from B and C respectively on AD and AD produced. Prove that BM = CN.
Triangles
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Answer
In △BMD and △CND,
BD = CD (As AD divides BC in two halves).
∠BMD = ∠CND (Both are equal to 90°)
∠BDM = ∠CDN (Vertically opposite angles)
∴ △BMD ≅ △CND by AAS axiom.
We know that corresponding sides of congruent triangles are equal.
∴ BM = CN.
Hence, proved that BM = CN.
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