Question

In given figure $AD$ and $BC$ are equal perpendiculars to a line segment $AB$. Show that $CD$ bisects $AB$

• A. $CD$ intersects $AB$ in any ratio
• B. $CD$ trisects $AB$
• C. $CD$ bisects $AB$
• D. Both B and C

Answer 1

Answer: (C)

$CD$ bisects $AB$

In $△AOD$ and $△BOC$

$\angle AOD=\angle BOC$ {vertical opposite angle}

$\angle DAO=\angle CBO={90}^{\circ }$

$BC=AD$ {Given}

So,

$△AOD\cong △BOC$ {AAS congruence}

$BO=AO$ {CPCT}

Hence, it is proved that $CA$ bisect $AB$.