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AD and BC are equal, perpendiculars to a line segment AB. Show that CD bisects AB.

AD and BC are equal, perpendiculars to a line segment AB. Show that CD bisects AB. NCERT Class 9 Mathematics CBSE Solutions.

Triangles

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Answer

Given :

⇒ AD = BC

From figure,

⇒ AD ⊥ AB, ∠OAD = 90°

⇒ BC ⊥ AB, ∠OBC = 90°

In △ BOC and △ AOD,

⇒ ∠BOC = ∠AOD (Vertically opposite angles are equal)

⇒ ∠OBC = ∠OAD (Each equal to 90°)

⇒ BC = AD (Given)

∴ △ BOC ≅ △ AOD (By A.A.S. congruence rule)

We know that,

Corresponding parts of congruent triangles are equal.

∴ BO = AO (By C.P.C.T.)

Hence, proved that CD bisects AB and O is the mid-point of AB.

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