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In this problem, \(ABEF\) is a trapezoid with \(AB\) and \(DC\) as the parallel sides. Given that \(AB = 14\) and \(DC = 24\), we are to find the length of \(EF\), which is the midline (or the line segment connecting the midpoints of the non-parallel sides) of the trapezoid.

In a trapezoid, the length of the midline \(EF\) is the average of the lengths of the two parallel sides. This can be calculated with the formula:
\[
EF = \frac{AB + DC}{2}
\]

Substituting the given values:
\[
EF = \frac{14 + 24}{2} = \frac{38}{2} = 19
\]

So, \(EF = 19\).

Would you like further details or have any questions?

Here are some related questions to explore:
1. What is the significance of the midline in a trapezoid?
2. How does the midline relate to the area of a trapezoid?
3. What would happen if \(AB\) and \(DC\) were equal in length?
4. Can this method be applied to any quadrilateral?
5. How would you find \(EF\) if \(AB\) or \(DC\) were missing?

**Tip:** In trapezoids, the midline always provides an average length between the parallel sides, which can help in area calculations and other geometric properties.

Learn how to find the length of the midline (EF) of a trapezoid where AB = 14 and DC = 24. Understand the midline theorem and the formula used to solve this geometry problem, suitable for middle school students in Grades 6-8.

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