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The problem is asking for the line(s) through point \( A \) that are perpendicular to line \( GH \) in the given 3D figure, which appears to be a rectangular prism or cuboid.

Let's analyze this:

- **Line \( GH \)** lies on the bottom face of the cuboid.
- We are asked to identify which line through point \( A \) is perpendicular to \( GH \).

We can now consider each of the listed lines:

1. **Line \( AH \)**: This line is diagonal across a side face of the cuboid, connecting point \( A \) to point \( H \), which is on the bottom face. This line would not be perpendicular to \( GH \) because both points \( A \) and \( H \) lie in planes that are not perpendicular to \( GH \).

2. **Line \( HE \)**: This line does not pass through point \( A \), so it is irrelevant to the question.

3. **Line \( AD \)**: This line is vertical and goes from point \( A \) straight down to point \( D \), forming a vertical edge. Since \( GH \) is horizontal and lies on the bottom plane of the cuboid, \( AD \) is perpendicular to \( GH \) because the vertical and horizontal planes are perpendicular.

4. **Line \( AG \)**: This line goes diagonally from point \( A \) to point \( G \). This line is not perpendicular to \( GH \) since both points \( A \) and \( G \) lie in different planes, but not at a right angle to each other.

### Conclusion:
The correct line through point \( A \) that is perpendicular to \( GH \) is **\( AD \)**.

Would you like further details or have any other questions? Here are 5 related questions to think about:

1. How do you determine the perpendicularity of lines in three-dimensional geometry?
2. What is the relationship between the planes that the lines lie in and the perpendicularity of the lines?
3. Can more than one line through a point be perpendicular to a given line?
4. How do diagonal lines like \( AH \) and \( AG \) differ from vertical or horizontal lines in terms of perpendicularity?
5. How can vector analysis be used to confirm perpendicularity in three-dimensional geometry?

**Tip:** In 3D geometry, perpendicular lines are often related to edges that lie in different planes that intersect at 90 degrees.

Name the line(s) through point A that appear perpendicular to GH in the given cuboid.

This problem involves identifying which line through point A is perpendicular to GH in a 3D cuboid. Learn to solve using 3D geometry concepts and theorems of perpendicularity between lines and planes.

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