Question

Property of intercepts made by three parallel lines on a transversal:

The ratio of the intercepts made on a transversal by three parallel lines is equal to the ratio of the corresponding intercepts made on any other transversal by the same three parallel lines.

Answer 1

Given: line l || line m || line n

The transversals x and y intersect these parallel lines at points A, B, C and P, Q, R respectively.

To Prove that: \(\cfrac{AB}{BC}=\cfrac{PQ}{QR}\) 

Construction: Draw seg AR to intersect line m at point H.

Proof: