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The problem asks to calculate the length of the segment joining the midpoints of segments \( GH \) and \( CD \) in a trapezoid. The given values are:

- Trapezoid \( ABCD \) is right-angled, with \( BC \parallel AD \).
- \( BC = 6 \), \( AD = 10 \), and the height \( CH \) is drawn.

We need to apply properties of trapezoids and midline theorems to solve this.

### Key steps:
1. The trapezoid is right-angled, with \( BC \parallel AD \), implying that the segment connecting the midpoints of two sides is related to the average of the parallel sides' lengths.

2. The length of the midsegment connecting the midpoints of the non-parallel sides of a trapezoid is given by the formula:

\[
\text{Midsegment length} = \frac{|BC - AD|}{2}
\]

Substitute the values:

\[
\text{Midsegment length} = \frac{|6 - 10|}{2} = \frac{4}{2} = 2
\]

Thus, the length of the segment connecting the midpoints of \( GH \) and \( CD \) is \( 2 \).

The correct answer is **B) 2**.

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Would you like further clarification on any step? 

Here are 5 related questions you might find useful:
1. How is the midsegment theorem used in trapezoid problems?
2. What are the properties of a right trapezoid?
3. Can the same approach be used for non-right trapezoids?
4. How do midpoints affect other shapes, such as triangles?
5. What would happen if the trapezoid were isosceles?

**Tip**: In geometry, always verify whether sides are parallel, perpendicular, or equal when applying theorems.

In a right trapezoid ABCD, BC || AD, the height CH is drawn. Calculate the length of the segment connecting the midpoints of GH and CD, given BC = 6 and AD = 10.

Learn how to calculate the length of the segment connecting the midpoints of GH and CD in a right trapezoid, with given side lengths BC = 6 and AD = 10. This problem demonstrates the application of the midline theorem in trapezoids, suitable for Grades 8-10.

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