Question

closer (reflection)
\why do you think parallel lines always cut proportional parts, no matter how far apart they are?\

Explanation:

When parallel lines are intersected by transversals, similar triangles are formed. By the properties of similar triangles, the ratios of corresponding sides are equal. This leads to the proportionality of the segments cut on the transversals.

Answer:

Parallel lines cut proportional parts because of the properties of similar triangles formed by the parallel lines and transversals. When two or more parallel lines are cut by transversals, the corresponding angles are equal. This equality of angles ensures that the triangles formed are similar. In similar triangles, the ratios of corresponding sides are equal. So, the segments on the transversals between the parallel lines are in proportion.