Question

given \\(\overleftrightarrow{cd} \parallel \overleftrightarrow{fg}\\). enter segments in the blanks provided that would result in a true equation.

answer
\\(\frac{cd}{fg} = \frac{\square}{\square}\\)

Explanation:

Step1: Identify similar triangles

Since $\overline{CD} \parallel \overline{FG}$, $\triangle OEG \sim \triangle DEC$ by AA similarity (corresponding angles are congruent due to parallel lines and transversals).

Step2: Set up proportional sides

For similar triangles, corresponding sides are proportional. The side $\overline{CD}$ corresponds to $\overline{FG}$, $\overline{DE}$ corresponds to $\overline{OE}$, so:
$\frac{CD}{FG} = \frac{DE}{OE}$
(Note: Other valid proportional pairs like $\frac{CE}{GE}$ also work, $\frac{DE}{OE}$ is one correct example)

Answer:

$\frac{DE}{OE}$ (or $\frac{CE}{GE}$, $\frac{CD}{FG} = \frac{OD}{OG}$ are also valid correct answers)