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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 тИЖBOC and тИЖAOD, we have
тИаBOC = тИаAOD
BC = AD [Given]
тИаBOC = тИаAOD [Vertically opposite angles]
тИ┤ тИЖOBC тЙЕ тИЖOAD [By AAS congruency]
тЗТ OB =OA [By C.P.C.T.]
i.e., O is the mid-point of AB.
Thus, CD bisects AB.

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