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  1. #1
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    vector , geometry

    In triangle PQR, the line ST is drawn parallel to QR so that PS= 3SQ. prove that PT = 3TR
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  2. #2
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    Quote Originally Posted by Tweety View Post
    In triangle PQR, the line ST is drawn parallel to QR so that PS= 3SQ. prove that PT = 3TR
    1. Let PT = k \cdot TR

    2. You are dealing with similar triangles. So use proportion:

    \dfrac{PS}{PS + SQ} = \dfrac{PT}{PT + TR}

    3. Substitute

    PS= 3 \cdot SQ ...... and ...... PT = k \cdot TR

    \dfrac{3 \cdot SQ}{3 \cdot SQ + SQ} = \dfrac{k \cdot TR}{k \cdot TR + TR}

    \dfrac{3 \cdot SQ}{4 \cdot SQ } = \dfrac{k \cdot TR}{(k+1) \cdot TR }

    \dfrac{3}{4 } = \dfrac{k}{(k+1)  } ~\implies~3(k+1) = 4k ~\implies~\boxed{3=k}
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  3. #3
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    thanks so much for that, I would have never figured out how to prove it!
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