Question

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

bisects AB.​

Answer 1

Step-by-step explanation:

In triangle BOC and AOD

DA = BC ( given)

angle DAO = CBO ( each 90)

angle AOD = BOC ( vertically opposite angles)

therefore , triangle BOC congruent AOD

implies, OC = OD

therefore CD bisects AB

Answer 2

Question :-

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

Answer :-

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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