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.

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, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

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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