Question

which construction might this image result from?
a.
construction to copy a line segment
b.
construction of a perpendicular bisector
c.
construction of a perpendicular to a line through a given point on the line
d.
construction of a line parallel to an existing line
e.
construction of a perpendicular to a line through a given external point

Explanation:

• Option A: Copying a line segment involves creating a segment of the same length as another. The image does not show this process.
• Option B: A perpendicular bisector construction would involve a line segment and a line that bisects it at a right - angle. The given image does not depict a line segment being bisected.
• Option C: Construction of a perpendicular to a line through a given point on the line would start with a point on the line. Here, point \(A\) is external.
• Option D: When constructing a line parallel to an existing line, we use the properties of angles (such as corresponding angles). The arcs (as in the image) are part of the process to ensure the parallelism (by creating equal angles).
• Option E: Construction of a perpendicular to a line through a given external point would result in a right - angle between the original line and the constructed line. The image does not show a right - angle construction.

Answer:

D. construction of a line parallel to an existing line