Question

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

Answer 1

⠀⠀ıllıllı uoᴉʇnloS ıllıllı

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In ∆BOC and ∆AOD, We have:

∠BOC = ∠AOD

BC = AD [Given]

∠BOC = ∠AOD [Vertically opposite angles]

∴ ∆OBC ≅ ∆OAD [By AAS congruency]

➠ OB = OA [By C.P.C.T.]

i.e., O is the mid-point of AB.

• Thus, CD bisects AB.

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Answer 2

Answer:

Here, we can say that

∠BOC = ∠AOD                           [Vertically Opposite Angles]

∠OBC = ∠OAD = 90°

AD = BC                                [Given]

∴ΔBOC ≅ ΔAOD

So, OB = OA             (C.P.C.T)