Question

AD and BC are equal perpendiculars to a line segment AB (see Fig). Show that CD bisects AB.

Answer 1

In ∆BOC and ∆AOD,

∠BOC = ∠AOD (Vertically opposite angles)

∠CBO = ∠DAO (Each 90º)

BC = AD (Given)

∴ ∆BOC ≅∆AOD (AAS congruence rule)

∴ BO = AO (By CPCT)

⇒ CD bisects AB.