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AD and BC are equal perpendiculars …

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

Posted by Ashi Thakur 6 years, 4 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given: AD and BC are equal perpendiculars to a line segment AB.
To Prove: CD bisects AB
Proof : In OAD and OBC
{tex}\angle{/tex}AOD = {tex}\angle{/tex}BOC ...[Vertically opposite angles]
{tex}\angle{/tex}OAD = {tex}\angle{/tex}OBC ...[each 90°]
AD = BC ...[Given]
{tex}\therefore{/tex} DOAD {tex}\cong{/tex} DOBC ...[By AAS property]
{tex}\therefore{/tex} OA = OB ...[c.p.c.t.]
{tex}\therefore{/tex} CD bisects AB

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