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

Answer 1

In given fig join AR
which cut BQ at X.

In triangle ACR , BX||CR
(by basic proportionality theorem)

AB/BC = AX/XR .....(1)

in triangle APR, XQ||AP
(by basic proportionality theorem)

PQ/QR = AX/XR .....(2)

from (1) and (2)
we get,
AB/BC = PQ/QR