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Question
AD and BC are equal perpendiculars to a line segment AB. If AD and BC are on different sides of AB prove that CD bisects AB.
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Solution
In ΔAOD and ΔBOC,
∠ AOD = ∠ BOC ....(vertically opposite angles)
∠ DAO = ∠ CBO ....(each 90°)
AD = BC ....(given)
∴ ΔAOD ≅ ΔBOC ...(by AAS congruence criterion)
⇒ AO = BO ...(c.p.c.t.)
⇒ O is the mid-point of AB.
Hence, CD bisects AB.
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