Question

triangle fgh is formed by connecting the midpoints of the side of triangl cde. the lengths of the sides of triangle cde are shown. what is the length of fg? figures not necessarily drawn to scale.

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
In \(\triangle CDE\), since \(F\) and \(G\) are midpoints, \(FG\) is a mid - segment.

Step2: Identify the corresponding side

The side corresponding to \(FG\) is \(CE\).
Given \(CE = 10\).

Step3: Calculate the length of \(FG\)

By the mid - segment theorem, \(FG=\frac{1}{2}CE\).
Substitute \(CE = 10\) into the formula: \(FG=\frac{1}{2}\times10\).

Answer:

\(5\)