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Question
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that TP:TQ = TR:TS
Solution
Consider ΔPTQ and ΔRTS,
`"PT"/"TR" = "QT"/"TS" = (1)/(2)` ...(Given)
∠PTQ = ∠RTS ...(Vertically Opposite angles)
⇒ ΔPTQ ∼ ΔRTS ...(SAS criterion for Similarity)
⇒ `"TP"/"TQ" = "TR"/"TS"`. ...(Rearranging the terms)
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