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AD and BC are equal perpendicular …

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AD and BC are equal perpendicular to a line segment AB Show that CD bisect AB

    • Posted by Angel Koddikar 5 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

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

    <hr />

    Given: AD and BC are equal perpendiculars to a line segment AB.
    To Prove: CD bisects AB.
    Proof: In ∆O AD and ∆OBC
    AD = BC    | Given
    ∠OAD = ∠OBC    | Each = 90°
    ∠AOD = ∠BOC
    | Vertically Opposite Angles
    ∴ ∠OAD ≅ ∆OBC    | AAS Rule
    ∴ OA = OB    | C.P.C.T.
    ∴ CD bisects AB.

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