Mathematics
In the adjoining figure, BM and DN are perpendiculars to the line segment AC. If BM = DN, prove that AC bisects BD.
Triangles
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Answer
In △BEM and △DEN,
BM = DN (Given).
∠BME = ∠DNE (Both are equal to 90°)
∠BEM = ∠DEN (Vertically opposite angles)
∴ △BEM ≅ △DEN by AAS axiom.
We know that corresponding parts of congruent triangles are equal.
∴ DE = BE.
Since, DE = BE it means that AC bisects BD at E.
Hence, proved that AC bisects BD.
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