Question

question 1 of 25

to construct a parallel to a line through a point not on the line using paper folding, you can perform the ______ construction twice.

a. angle bisector
b. congruent angle
c. midpoint of a line segment
d. perpendicular line segment

Explanation:

Analyze the geometric goal

To construct a line parallel to a given line \(l\) through a point \(P\) not on \(l\) using paper folding.

Evaluate paper folding operations

1. First fold: Fold the paper so that the line \(l\) aligns onto itself through point \(P\). This creates a crease perpendicular to line \(l\) passing through \(P\).
2. Second fold: Fold the paper again so that this new crease aligns onto itself through point \(P\). This creates a second crease perpendicular to the first crease at point \(P\).

Determine the final relationship

Since two lines perpendicular to the same line are parallel to each other, the second crease is parallel to the original line \(l\) and passes through \(P\). This process uses the perpendicular line construction twice.

Answer:

• A. angle bisector
• B. congruent angle
• C. midpoint of a line segment
• D. perpendicular line segment (Correct answer)