Question

use the diagram to complete the proportion. \\(\frac{\square}{bd} = \frac{cg}{ce}\\)

Explanation:

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

When a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides those sides proportionally. In the given diagram, the parallel lines create similar - proportion relationships.

Step2: Identify the corresponding segments

We have three parallel lines. For the proportion \(\frac{BD}{CE}\), the corresponding segment for \(CG\) is \(DF\).

Answer:

\(DF\)