Question

AD and BC are equal and perpendicular to a line segment AB.show that CD bisects AB​

Answer 1

Step-by-step explanation:

Given: AD ⊥ AB, BC ⊥ AB, and AD = BC

To Prove: CD bisects AB or OA = OB

We can show that the two triangles OBC and OAD are congruent by using AAS congruency rule and then we can say corresponding parts of congruent triangles will be equal.



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.

Answer 2

AD and BC are equal perpendiculars to a line segment AB