Parallel line segments *AB* and *CD* are reflected across the perpendicular bisector of *AB*. Select all the true statements.


Let's analyze the scenario carefully:

You have parallel line segments \( AB \) and \( CD \), and they are reflected across the **perpendicular bisector of \( AB \)**.

### Key Observations:
1. **Perpendicular bisector reflection**:
   - A reflection across the perpendicular bisector of a segment maps the segment to itself (or its mirror image) but reverses orientation.
   - Since \( AB \) is reflected across its **own** perpendicular bisector, it will map onto itself or onto a segment that is exactly the same as \( AB \), just flipped.

2. **Effect on parallel line \( CD \)**:
   - The reflection will map each point on \( CD \) across the perpendicular bisector of \( AB \).
   - If \( CD \) is sufficiently far away from \( AB \), the image of \( CD \) will still be parallel to the image of \( AB \), but on the opposite side of the bisector.

3. **Specific properties**:
   - The distances between \( AB \) and \( CD \), before and after the reflection, will remain the same if they were initially parallel.
   - \( CD \)'s orientation relative to the perpendicular bisector may change, depending on its position.

### True Statements:
Now, based on the reflection across the perpendicular bisector of \( AB \), let's summarize the true statements that typically hold in this situation:
- \( AB \) maps onto itself (or a mirror image of itself).
- \( CD \) remains parallel to \( AB \) after the reflection if the original \( CD \) was parallel and aligned properly with \( AB \).
- The relative distance between \( AB \) and \( CD \) before and after reflection will remain the same if the segments are parallel.
- The reflection preserves distances and angles, so parallelism is maintained if no other rotations or distortions occur.

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### Related Questions:
1. What happens if \( CD \) is not parallel to \( AB \)?
2. How would the situation change if the reflection were across the perpendicular bisector of \( CD \)?
3. What if \( CD \) is equidistant from \( AB \) on both sides of the perpendicular bisector?
4. Can this reflection be described algebraically using coordinate geometry?
5. How does the reflection of a point work when reflected across a perpendicular bisector?

#### Tip:
Remember that reflections across a line always preserve distances and angles, but they reverse orientations!

Parallel line segments AB and CD are reflected across the perpendicular bisector of AB. Select all the true statements.

Explore how parallel line segments AB and CD behave when reflected across the perpendicular bisector of AB. This problem covers key geometric concepts such as reflection, parallel lines, and the perpendicular bisector theorem. Suitable for students in Grades 9-12.

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