Question

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

Answer 1

In triangle OAD & OBC
AD=BC (GIVEN)
<OAD=<OBC (EACH=90*)
<AOD=<BOC (VERTICLE OPP ANGLE)
THEREFORE,
TRIANGLE ODA=OCB (AAS CRITERIA)

OA=OB (CPCT)

So, CD bisects AB.

this is your answer

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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