https://file.aiquickdraw.com/mathbot/file/17260728456526pnznkzw.jpg

In the problem, we are given that:
- Line segment \( \overline{AM} \perp \overline{MN} \) and
- Line segment \( \overline{UK} \perp \overline{MN} \).

We are asked what other facts can be concluded based on this information.

Looking at the diagram:
- \( \overline{AM} \perp \overline{MN} \) means that line \( \overline{AM} \) is perpendicular to line \( \overline{MN} \), forming a right angle at point \( M \).
- \( \overline{UK} \perp \overline{MN} \) means that line \( \overline{UK} \) is also perpendicular to line \( \overline{MN} \), forming a right angle at point \( K \).

Now let's analyze the options provided:

1. **\( \overline{AL} \parallel \overline{UK} \)**:  
   This is likely false, as there is no direct evidence in the diagram that \( \overline{AL} \) is parallel to \( \overline{UK} \). Both lines seem to be vertical, but it's not explicitly stated that they are parallel.

2. **\( m \angle MBK = 90^\circ \)**:  
   This statement is **true**. Since both \( \overline{AM} \) and \( \overline{UK} \) are perpendicular to \( \overline{MN} \), and point \( B \) lies between \( M \) and \( K \), the angle \( MBK \) must be a right angle, \( 90^\circ \).

3. **\( \overline{MN} \parallel \overline{LT} \)**:  
   This is likely **true**. \( \overline{MN} \) and \( \overline{LT} \) are horizontal lines that appear to be parallel in the diagram.

4. **\( \overline{AL} \perp \overline{LT} \)**:  
   This is likely false. There is no indication that \( \overline{AL} \) is perpendicular to \( \overline{LT} \) from the given information.

Thus, the correct conclusion is that \( m \angle MBK = 90^\circ \), and possibly \( \overline{MN} \parallel \overline{LT} \) (though that option was not checked in this screenshot).

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Do you have any questions or want more details on the analysis?

### Relative Questions:
1. What geometric properties define parallel lines in this context?
2. How can we prove that \( \overline{MN} \parallel \overline{LT} \)?
3. What is the significance of perpendicular lines in geometry?
4. How can angles be classified based on their measure?
5. How do we deduce that \( m \angle MBK = 90^\circ \)?

### Tip:
When analyzing geometric diagrams, always look for right angles and parallel lines, as they often provide clues to other relationships in the figure.

Rodrigo knows that AM ⊥ MN and UK ⊥ MN. What other facts can Rodrigo conclude are true? Select each correct answer.

Learn how to identify perpendicular and parallel lines in geometric figures. Understand the concept of right angles and the relationships between intersecting lines. This problem involves applying the Perpendicular Line Theorem and the Parallel Postulate.

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