AD and BCare equal perpendicular to a line segment AB. show that CD bisects AB
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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
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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