Question

polygon abcd reflects about line mn to make polygon efgh. what is the length of \\(\overline{fg}\\)?

Explanation:

Step1: Recall Reflection Property

Reflection is a rigid transformation, so corresponding sides of the original polygon and its image are congruent.

Step2: Identify Corresponding Sides

In polygon \(ABCD\) and its reflection \(EFGH\), side \(BC\) in \(ABCD\) corresponds to side \(FG\) in \(EFGH\).

Step3: Determine Length of \(BC\)

From the diagram, the length of \(BC\) is \(2\).

Step4: Conclude Length of \(FG\)

Since reflection preserves side lengths, \(FG = BC = 2\).

Answer:

\(2\)