To determine the relationship between the line segments \(\overline{A B}\) and \(\overline{C D}\), we need to analyze their slopes and respective positions. Here's a step-by-step solution:
1. Calculate the slope of \(\overline{A B}\):
- Coordinates: \(A(3,6)\) and \(B(8,7)\).
- Formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
[tex]\[
\text{slope of } \overline{A B} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
- Substituting the values:
[tex]\[
\text{slope of } \overline{A B} = \frac{7 - 6}{8 - 3} = \frac{1}{5}
\][/tex]
2. Calculate the slope of \(\overline{C D}\):
- Coordinates: \(C(3,3)\) and \(D(8,4)\).
- Using the same formula:
[tex]\[
\text{slope of } \overline{C D} = \frac{4 - 3}{8 - 3} = \frac{1}{5}
\][/tex]
3. Compare the slopes:
- Slope of \(\overline{A B}\) = \(\frac{1}{5}\).
- Slope of \(\overline{C D}\) = \(\frac{1}{5}\).
4. Since the slopes of \(\overline{A B}\) and \(\overline{C D}\) are equal:
- The lines are parallel if their slopes are equal.
Therefore, the correct statement is:
A. \(\overline{A B} \parallel \overline{C D}\).
So, the relationship between the segments is that [tex]\(\overline{A B}\)[/tex] is parallel to [tex]\(\overline{C D}\)[/tex].
