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  • AD and BC are equal perpendiculars to a line segment AB (see Fig.). Show that CD bisects AB.

3.  \small AD and \small BC are equal perpendiculars to a line segment \small AB (see Fig.). Show that  \small CD bisects \small AB.

  

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In the given figure consider \DeltaAOD  and  \DeltaBOC.

(i)  AD  =  BC               (given)

(ii)  \angle A   =  \angle B            (given that the line AB is perpendicular to AD and BC)

(iii)  \angle AOD  =  \angle BOC (vertically opposite angles).

Thus by AAS Postulate, we have  \Delta AOD\ \cong \ \Delta BOC

Hence by c.p.c.t. we can write :  AO\ =\ OB

And thus CD bisects AB.

Posted by

Devendra Khairwa

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