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