To solve this geometry question, let's break down the steps and examine the concept involved.
When you are asked to find a perpendicular line segment from a point to a line, you can achieve this using a method called "paper folding." Here’s the detailed process:
1. Identify the Point: Let's denote the point as [tex]\( P \)[/tex].
2. Identify the Line: Let's call this line [tex]\( l \)[/tex].
3. Folding the Paper: Imagine that you are folding the paper such that the point [tex]\( P \)[/tex] lies exactly on the line [tex]\( l \)[/tex].
During this folding process, the fold line itself forms a perpendicular to the line [tex]\( l \)[/tex] passing through the point [tex]\( P \)[/tex]. This is because:
- When you fold the paper, any point on the paper is mirrored to match with another point due to the properties of geometric reflection.
- The fold line is equidistant from the two matched points (in this case, the point [tex]\( P \)[/tex] and its image on the line [tex]\( l \)[/tex]) and is at the shortest distance possible between them, which is the definition of a perpendicular line.
Thus, the fold line inherently becomes a line segment from the point [tex]\( P \)[/tex] to the line [tex]\( l \)[/tex] that is perpendicular to [tex]\( l \)[/tex].
In conclusion:
- If you fold the paper such that the identified point lies exactly on the line, the crease created by this fold will be perpendicular to the line.
Therefore, the statement "To find a perpendicular line segment from a point to a line, fold the paper so that the two endpoints of the segment match up" is:
○ A. True
