Question

16. AD and BC are equal perpendiculars to a line
segment AB. If AD and BC are on different
sides of AB prove that CD bisects AB.​

Answer 1

Answer:

From figure,

In △OAD & △OBC

∠B=∠A.. .....(90

o

)

And,

∠D=∠C

And,

AD=BC

So, byASA congruence criterion rule,

△OAD is congruent to △OBC

Therefore,

OA=OB

Hence,

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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