Question

D and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB​

Answer 1

Consider two triangles △ BOC and △ AOD,

In △ BOC and △ AOD,

∠BOC = ∠AOD (Vertically opposite angles)

∠CBO = ∠DAO (Each 90º, since AD and BC are ⊥ to AB)

BC = AD (Given)

∴ △BOC ≅ △AOD (AAS congruence rule)

∴ BO = AO (By CPCT)

Thus, CD bisects AB and O is the mid-point of AB.

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