Question

AD and BC are perpendiculars to line segment AB as given in the figure, show that CD bisects AB​

Answer 1

CD bisects AB means we have to prove BO= AO
in triangle BOC and triangle AOD
angle B cong. angle A (each 90°)
side BC cong. side AD ( given)
angle BOC cong. angle AOD( vertically opposite angle)
therefore, ∆BOC cong. ∆AOD(ASA test)
side BO= side AO ( Cong. sides of cong. triangle)
hence proved

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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