Question

triangle fgh is formed by connecting the midpoints of the side of triangle cde. the lengths of the sides of triangle cde are shown. what is the length of \\(\overline{hc}\\)? figures not necessarily drawn to scale.

Explanation:

Step1: Identify Midsegment Property

In a triangle, the segment connecting the midpoints of two sides is a midsegment, which is parallel to the third side and half its length. Here, \( H \) is the midpoint of \( CE \) (since \( FG H \) connects midpoints of \( CDE \)'s sides, and \( CE = 8 \)). Wait, actually, looking at the triangle \( CDE \), \( H \) is the midpoint of \( CE \), and we need to find \( HC \). Since \( H \) is the midpoint, \( HC=\frac{CE}{2}\).

Step2: Calculate \( HC \)

Given \( CE = 8 \), so \( HC=\frac{8}{2}=4 \).

Answer:

\( 4 \)