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9th Class Mathematics Geometry Question Bank Geometry

  • question_answer
    If \[l,m,n\] are three parallel lines and the transversals \[{{t}_{1}}\] and \[{{t}_{2}}\] cut the lines \[l,m,n\] at the points A, B, C and P, Q, R as shown in the figure, then

    A) \[\frac{AB}{BC}=\frac{PQ}{QR}\]

    B) \[\frac{AB}{QR}=\frac{BC}{PQ}\]

    C) \[\frac{AP}{BQ}=\frac{BQ}{CR}\]

    D) \[\frac{AB}{PQ}=\frac{AP}{BQ}\]

    Correct Answer: A

    Solution :

      Drop perpendicular ADE and PST from A and P to the other lines m and n. From two similar As ABD and ACE,                 \[\frac{AB}{AC}=\frac{AD}{AE}\]                               ?..(i) Also from similar \[\Delta \,s\] PSQ and PTB,                 \[\frac{PQ}{PR}=\frac{PS}{PT}\]                                ??(ii) Since \[AD=PS\] and \[AE=PT,\]therefore                 \[\frac{AB}{AC}=\frac{PQ}{PR}\] Applying dividendo,                 \[\frac{AB}{AC-AB}=\frac{PQ}{PR-PQ}\] or            \[\frac{AB}{BC}=\frac{PQ}{OR}\]


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