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.