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AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.

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#### Solution

In ΔBOC and ΔAOD,

∠BOC = ∠AOD (Vertically opposite angles)

∠CBO = ∠DAO (Each 90º)

BC = AD (Given)

∴ ΔBOC ≅ ΔAOD (AAS congruence rule)

∴ BO = AO (By CPCT)

⇒ CD bisects AB.

Concept: Criteria for Congruence of Triangles

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