Two similarity pairs in a trapezium

Two similarity pairs in a trapezium

Secondary 2
TGM Original Questions

In trapezium \(WXYZ\), \(WX\parallel ZY\). Diagonals \(WY\) and \(XZ\) meet at \(S\). Point \(P\) lies on \(WZ\), point \(T\) lies on \(WY\), and \(PT\parallel ZY\). Given \(WX=\frac35ZY\) and \(ZP=\frac23ZW\):

  1. name two pairs of similar triangles
  2. find
    1. \(SX/SZ\),
    2. \(PT/ZY\).

Solution:

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Answer:(a) \(\triangle WXS\sim\triangle YZS\), \(\triangle WPT\sim\triangle WZY\); (b)(i) \(3/5\); (ii) \(1/3\).

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