Question: User: Question content area top Part 1 Prove the following theorem. Any rigid motion can be expressed as a composition of reflections. Question content area bottom Part 1 Any rigid motion must be a\u200b translation, a\u200b reflection, a\u200b rotation, or a glide reflection. Consider these one at a time. Which of the following is true of\u200b translations? A. Any translation can be expressed as a composition of reflections across three lines whose single intersection point is halfway between any point and its image. B. Any translation can be expressed as a composition of reflections across two parallel lines. C. Any translation can be expressed as a composition of reflections across two perpendicular lines that intersect halfway between any point and its image. D. Any translation can be expressed as a composition of reflections across three parallel lines. E. Any translation can be expressed as a composition of reflections across two lines whose intersection point is halfway between any point and its image.

1. **State the problem:** We need to determine which statement correctly describes how any translation can be expressed as a composition of reflections. 2. **Recall the theorem:** Any rigid motion (isometry) in the plane can be expressed as a composition of reflections. 3. **Focus on translations:** A translation moves every point by the same distance in the same direction. 4. **Key fact about translations and reflections:** - A translation can be represented as the composition of two reflections across two parallel lines. - The distance between these two parallel lines is half the magnitude of the translation vector. 5. **Explanation:** - Reflecting a point across the first line moves it to an intermediate position. - Reflecting this image across the second parallel line moves it to the final translated position. - The composition of these two reflections results in a translation. 6. **Check the options:** - A: Three lines with a single intersection point — incorrect for translation. - B: Two parallel lines — correct. - C: Two perpendicular lines — this produces a rotation, not a translation. - D: Three parallel lines — unnecessary and incorrect. - E: Two lines intersecting at a point — this produces a rotation, not a translation. **Final answer:** **B. Any translation can be expressed as a composition of reflections across two parallel lines.**