Question

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Explanation:

Step1: Check the proportionality for the first triangle

For the first triangle, we check if \(\frac{PS}{SQ}=\frac{PT}{TR}\).
\(PS = 9.7\), \(SQ=19.3\), \(PT = 8\), \(TR = 17\)
\(\frac{PS}{SQ}=\frac{9.7}{19.3}\approx0.5\), \(\frac{PT}{TR}=\frac{8}{17}\approx0.47\)
Since \(\frac{9.7}{19.3}
eq\frac{8}{17}\), \(ST\) is not parallel to \(QR\) in the first triangle.

Step2: Check the proportionality for the second triangle

For the second triangle, we check if \(\frac{PS}{SQ}=\frac{PT}{TR}\).
\(PS = 8.5\), \(SQ = 20.5\), \(PT=6.5\), \(TR = 18.5\)
\(\frac{PS}{SQ}=\frac{8.5}{20.5}=\frac{85}{205}=\frac{17}{41}\approx0.415\)
\(\frac{PT}{TR}=\frac{6.5}{18.5}=\frac{65}{185}=\frac{13}{37}\approx0.351\)
Since \(\frac{8.5}{20.5}
eq\frac{6.5}{18.5}\), \(ST\) is not parallel to \(QR\) in the second triangle.

Answer:

Neither of the triangles has \(ST\) parallel to \(QR\).