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Question
In the following diagram, lines l, m and n are parallel to each other. Two transversals p and q intersect the parallel lines at points A, B, C and P, Q, R as shown.
Prove that : `(AB)/(BC) = (PQ)/(QR)`
Solution
Join AR.
In ΔACR, BX || CR.
By Basic Proportionality theorem,
`(AB)/(BC) = (AX)/(XR)` ...(1)
In ∆APR, XQ || AP.
By Basic Proportionality theorem,
`(PQ)/(QR) = (AX)/(XR)` ...(2)
From (1) and (2), we get,
`(AB)/(BC) = (PQ)/(QR)`
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