Question

to find a segment parallel to another segment and through a given point, fold a piece of paper so that the fold goes through the point and the pieces of the segment on either side of the fold match up.

a. true
b. false

Explanation:

Analyze the folding operation

Using the Paper Folding Constructions knowledge point:
Folding a piece of paper so that the pieces of a segment on either side of the fold match up creates a fold line that is perpendicular to that segment. If the fold also goes through a given point, this creates a perpendicular line through that point, not a parallel line.

Determine the geometric result

To construct a parallel line through a point, one must fold a perpendicular line first, and then fold a second perpendicular line to the first fold through the given point. A single fold matching the segment onto itself creates a perpendicular line. Therefore, the statement is false.

Answer:

• A. True
• B. False (Correct answer)