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Question:

In given figure AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.

Solution:

In ΔBOC and ΔAOD, ∠BOC = ∠AOD (Vertically opposite angles) ∠CBO = ∠DAO (Each 90°) BC = AD (Given) Therefore, ΔBOC ≅ ΔAOD (AAS congruence rule) Therefore, BO = AO (By CPCT) => CD bisects AB.