To solve the problem, let's analyze the diagram and the given data step by step:

Given:

1. AB = 10 cm
2. DC = 15 cm
3. EF is the line that connects the midpoints of AB and DC.

Key Concept:

The segment EF is the midsegment of the trapezoid formed by lines AB and DC. A midsegment in a trapezoid is parallel to the bases and its length is the average of the two bases' lengths.

The formula for the midsegment (EF) is: $\text{Length of EF} = \frac{\text{Length of AB} + \text{Length of DC}}{2}$

Substitution:

$\text{Length of EF} = \frac{10 + 15}{2} = \frac{25}{2} = 12.5 \, \text{cm}$

The correct answer for the length of EF is 12.5 cm.

Do you have further questions or would you like details about the properties of midsegments?

Related Questions:

1. How do you calculate the midsegment of a triangle instead of a trapezoid?
2. What are the properties of parallel lines in a trapezoid?
3. How do midsegments relate to other geometric figures?
4. Can you calculate EF if the trapezoid is rotated?
5. What if the lengths of AB and DC were variable?

Tip:

Always verify if the given figure is a trapezoid and ensure the midpoints are connected when using the midsegment formula!