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Question
In the given figure, AD and BC are equal perpendiculars to a line segment AB.
Show that CD bisects AB.
In the given figure, AD and BC are equal perpendiculars to a line segment AB.
Show that CD bisects AB.
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Solution
In triangle OAD & OBC
AD=BC (GIVEN)
∠OAD=∠OBC=90o
∠AOD=∠BOC (VERTICLE OPP ANGLE)
THEREFORE,
TRIANGLE ODA=OCB (AAS CRITERIA)
OA=OB (CPCT)
So, CD bisects AB.
In triangle OAD & OBC
AD=BC (GIVEN)
∠OAD=∠OBC=90o
∠AOD=∠BOC (VERTICLE OPP ANGLE)
THEREFORE,
TRIANGLE ODA=OCB (AAS CRITERIA)
OA=OB (CPCT)
So, CD bisects AB.
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