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Question
In the figure, PR || SQ. If PR = 10cm, PT = 5cm, TQ = 6cm and ST = 9cm, calculate RT and SQ.
Solution
In ΔPRT and ΔSQT
∠PTR = ∠STQ ...(veriically opposite angles)
∠RPT = ∠SQT ...(alternate angles ∵ PR || SQ)
∴ ΔPRT ≅ ΔSQT
⇒ `"RT"/"PT" = "ST"/"TQ"`
⇒ `"RT"/(5) = (9)/(6)`
⇒ RT = `(5 xx 9)/(6)`
⇒ RT = 7.5cm
Also,
`"PT"/"PR" = "TQ"/"SQ"`
⇒ `(5)/(10) = (6)/"SQ"`
⇒ SQ = `(6 xx 10)/(5)`
⇒ SQ = 12cm.
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