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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 5 years, 3 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Sia ? 5 years, 3 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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