Question

given ( overline{gh} ) is a midsegment and ( overline{gh} ) is 7, find the length of ( overline{cf} ).
( cf = )

Explanation:

Step1: Recall the midsegment theorem

In a triangle, the midsegment is parallel to the third side and half its length. Here, \( \overline{GH}\) is a midsegment and \( \overline{CF}\) is the third side.

Step2: Apply the formula

Let \( GH = 7\). By the midsegment theorem \( GH=\frac{1}{2}CF\). Then \( CF = 2\times GH\).
Substitute \( GH = 7\) into the formula: \( CF=2\times7\).

Answer:

\(14\)