AD AND BC ARE EQUAL PERPENDICULAR TO A LINE SEGMENT AB.(SHOW THAT CD BISECTS AB)
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AD AND BC ARE EQUAL PERPENDICULAR TO A LINE SEGMENT AB.(SHOW THAT CD BISECTS AB)..?
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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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