Question

quiz: polygons and triangles
which one of the following proportions is true for the segments shown in the figure if lines a, b, and c are parallel to each other?
a) \\( \frac { a c } { a e } = \frac { b d } { b f } \\)

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

When three parallel lines \(a\), \(b\), \(c\) are cut by two transversals, the ratios of the corresponding segments are equal.
For transversals \(AE\) and \(BF\), we have \(\frac{AC}{AE}=\frac{BD}{BF}\) because of the property of parallel lines cutting transversals.

Answer:

A. \(\frac{AC}{AE}=\frac{BD}{BF}\)