Non parallel transversals that intersect parallel lines can intersect to form similar triangles. So the sides of these triangles will be proportional. Notice in the diagram to the right ∆ABC is formed by extending the transversals AB and AC.
The sides of this triangle (AB and AC) are cut proportionally. The proportionality theorem explains this relationship. The converse of this theorem is also true.
The following example uses the proportionality theorem to find missing side lengths. Copy the example and watch the help video if you need to see one worked out. Try the question below and check your solution to see if you understand the concept.
The proportionality relationship is true even when there are more than 2 parallel lines or segments. In the diagrams to the right there are multiply parallel lines so the transversals are cut into 3 proportional parts.