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Angle–Angle Similarity: Triangles in Lines \(𝑃𝑆𝑄\) and \(𝑃𝑇𝑅\)

Angle–Angle Similarity: Triangles in Lines \(𝑃𝑆𝑄\) and \(𝑃𝑇𝑅\)

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In the figure \(PSQ\) and \(PTR\) are straight lines and \(\angle PST=\angle PRQ\). \(PS=4\) cm, \(QR=10\) cm, \(RT=3\) cm, \(ST=5\) cm, \(PT=x\) cm and \(QS=y\) cm.

  1. Name a pair of similar triangles.
  2. Find the value of \(x\) and the value of \(y\).

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Answer:\(\text{(a)}\ \triangle PST\sim\triangle PRQ\) \(\text{(b)}\ x=5,\quad y=6\)

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