10th Class Mathematics Solved Paper - Mathematics-2015 Term-I

  • question_answer X and Y are points on the sides AB and AC respectively of a triangle ABC such that \[\frac{AX}{AB},AY=2\,cm\] and \[YC=6\,cm\]. Find whether \[XY\parallel BC\] or not.

    Answer:

                \[\frac{AX}{AB}=\frac{1}{4}\]
    i.e.,                               \[AX=1K,\text{ }AB=4K\]    (K- constant)
    \[\therefore BX=AB-AX\]
                            \[=4K-1K=3K\]
    Now,                 \[\frac{AX}{XB}=\frac{1K}{3K}=\frac{1}{3}\]
    And,                 \[\frac{AY}{YC}=\frac{2}{6}=\frac{1}{3}\]
                            \[\frac{AX}{XB}=\frac{AY}{YC}\]
    \[\therefore XY\parallel BC\]         (By converse of Thales? theorem)


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