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Question
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
Solution
In ΔBMR and DNR
BM = DN
∠BMR = ∠DNR = 90°
∠BRM = ∠DRN = ...(vertically opposite angles)
Hence, ∠MBR = ∠NDR ...(sum of angles of a triangle = 180°)
ΔBMR ≅ ΔDNR ...(ASR criteria)
Therefore, BR = DR
So, AC bisects BD.
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