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Math Help - geometry measurements

  1. #1
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    geometry measurements

    see attatched picture
    in the diagram AB is parallel to CD
    AB = OC = 12cm. OB = 10cm
    use similar triangles to calculate the length of CD
    Attached Thumbnails Attached Thumbnails geometry measurements-math.jpg  
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mrmann View Post
    see attatched picture
    in the diagram AB is parallel to CD
    AB = OC = 12cm. OB = 10cm
    use similar triangles to calculate the length of CD
    Since AB is parallel to CD, then
    angle ABO = angle DCO

    angle AOB = angle DOC
    because vertical angles are congruent.

    So, triangle ABO is similar to triangle DOC
    because two of their three angles are equal each to each.

    The two triangles are similar, and hence, proportional.
    By proportion,
    (here, be careful in your choosing what sides are corresponding to each triangles. For a guide, use the two congruent angles ABO and CDO.)
    AB/BO = CD/CO
    12/10 = CD/12
    Cross multiply,
    10(CD) = 12(12)
    CD = 144/10 = 14.4 cm ------answer.
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