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: $\dfrac{AB}{BC} = \dfrac{PQ}{QR}$

Join A and R. Let AR meet BQ at point D.

In ∆ACR, BD || CR.

By Basic proportionality theorem, we get

$\dfrac{AB}{BC} = \dfrac{AD}{DR}$ …..(1)

In ∆APR, DQ || AP.

By Basic proportionality theorem, we get

$\dfrac{PQ}{QR} = \dfrac{AD}{DR}$ …..(2)

From (1) and (2) we get :

$\dfrac{AB}{BC} = \dfrac{PQ}{QR}$

Hence proved that $\dfrac{AB}{BC} = \dfrac{PQ}{QR}$.