Question
AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB (See figure)
✓
Answer
In $\triangle$BOC and $\triangle$AOD,
$\angle$OBC = $\angle$OAD = 90° [Given]
$\angle$BOC = $\angle$AOD [Vertically Opposite angles]
BC = AD [Given]
$\therefore$ $\triangle$BOC $\cong$ $\triangle$AOD [By ASA congruency]
$\Rightarrow$ OB = OA and OC = OD [By C.P.C.T.]
$\angle$OBC = $\angle$OAD = 90° [Given]
$\angle$BOC = $\angle$AOD [Vertically Opposite angles]
BC = AD [Given]
$\therefore$ $\triangle$BOC $\cong$ $\triangle$AOD [By ASA congruency]
$\Rightarrow$ OB = OA and OC = OD [By C.P.C.T.]
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