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)`

Answer 1

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)`