AD and BC are equal perpendiculars to a line segment AB (see figure).

1.	AD and BC are equal perpendiculars to a line segment AB (see figure). Show that CD bisects AB.
Answer» In ∆OBC and ∆OAD ∵ ∠B = ∠A = 90° (as AD and BC are perpendiculars) and OB = OA (given) and ∠BOC = ∠AOD (vertically opposite angles) ∴ ∆OBC ≅ ∠OAD (by AAS congruence rule) => OA = OB (by c.p.c.t) => CD bisects AB Hence proved.

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

Answer»

In ∆OBC and ∆OAD

∵ ∠B = ∠A = 90°

(as AD and BC are perpendiculars)

and OB = OA (given)

and ∠BOC = ∠AOD

(vertically opposite angles)

∴ ∆OBC ≅ ∠OAD

(by AAS congruence rule)

=> OA = OB (by c.p.c.t)

=> CD bisects AB

Hence proved.