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Question
AD and BC are equal perpendiculars to a line segment AB (See the given figure). Show that CD bisects AB.
Solution
In △BOC and △AOD,
∠OBC = ∠OAD ...[Each 90° (Given)]
∠BOC = ∠AOD ...[Vertically opposite angles]
BC = AD ...[Given]
∴ △BOC ≌ △AOD ...[By AAS congruence rule]
⇒ OB = OA ...[Corresponding parts of congruent triangles]
i.e., O is the mid-point of AB.
So, CD bisects the line segment AB.
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