Ad and bc are equal perpendiculars to a line


Asked by admin @ in Math viewed by 284 People


AD and BC are equal perpendiculars to a line segment AB . show that CD bisects AB. ( by using a criteria)

Answered by admin @



\bf{\underline{Q.\: AD\: and \:BC \:are\: perpendiculars\:}} \bf{\underline{to\: a\: line\: segment\: AB. \:Show\: that\: }}
\bf{\underline{ CD\:bisects\: AB.}}

\mathbb{ SOLUTION }:

Given,
AD and BC are perpendiculars of AB.

\mathbb{ TO \:BE \:SHOWN }:
CD bisects AB

∠BOC = ∠DOC ( ∴ Vertically opposite angles )

DA = BC
∠B = ∠A = 90°

So, by \bf{AAS} congruence condition, ΔBOC ≅ ΔOAD

So,
now CO = OD
so, it bisects AB on point '\bf{O}'

OA = OB [ by \bf{CPCT} ]

➖➖➖➖➖➖➖➖➖➖➖➖➖

\bf{AAS} : Angle-Angle-side

\bf{CPCT} : Corresponding Parts of Congruent Triangles

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