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Question

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


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Solution

Given

ADand BC are equal perpendiculars to a line segment AB

To Prove

CD bisects AB

Proof

Two triangles ΔAOD and ΔBOC

AOD=BOC {Vertically opposite angles}………………. (i)

OAD=OBC {Given that they are perpendiculars}…. (ii)

AD=BC {As given}………………………………………………… (iii)

From above three equation both the triangle satisfies “AAS” congruency criterion

So, ΔAODΔBOC

AO and BO will be equal as they are corresponding parts of congruent triangles(CPCT).

So, AO=BO

Hence, CD bisectsAB at O.


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