Question

in the figure below, \\( \overline { c d } \\) is a bisector of \\( \overline { a b } \\), \\( \overline { c d } = 10 \\) feet, and \\( \overline { a b } = 10 \\) feet. what is the length, in feet, of \\( \overline { e b } \\)?

Explanation:

Step1: Recall the property of a bisector

A bisector divides a line segment into two equal parts. Since \(\overline{CD}\) is a bisector of \(\overline{AB}\), then \(AE = EB\).

Step2: Calculate the length of \(EB\)

Given \(AB = 10\) feet. Using the formula \(AB=AE + EB\) and \(AE = EB\) (from the bisector property), we substitute \(AE\) with \(EB\). So \(AB=EB + EB=2EB\).
Solving for \(EB\), we have \(EB=\frac{AB}{2}\).
Substituting \(AB = 10\) into the formula: \(EB=\frac{10}{2}=5\) feet.

Answer:

B. 5