Question

question 6 of 25
if you repeat the perpendicular line segment construction twice using paper folding, you can construct:
a. a parallel to a line through a point not on the line.
b. an angle congruent to a given angle.
c. the midpoint of a line segment.
d. an angle bisector.

Explanation:

Step1: Understand perpendicular line segment construction

When we do perpendicular line segment construction using paper - folding, we create a right - angle (\(90^{\circ}\)) with respect to a given line.

Step2: Analyze the effect of repeating the construction

If we repeat the perpendicular line segment construction (paper - folding) twice. Let's assume we have a line \(l\) and a point \(P\) not on the line \(l\).
First, we fold the paper to construct a perpendicular \(m\) to line \(l\). Then, we fold the paper again to construct a perpendicular \(n\) to the line \(m\).
By the property of perpendicular lines, if \(m\perp l\) and \(n\perp m\), then \(n\parallel l\) (because if two lines are perpendicular to the same line, then they are parallel to each other). So, repeating the perpendicular line segment construction twice using paper - folding allows us to construct a parallel to a line through a point not on the line.

• Option B: To construct an angle congruent to a given angle, we usually use the method of copying an angle (not just repeated perpendicular constructions).
• Option C: To find the mid - point of a line segment, we use the method of folding the line segment onto itself so that the two endpoints coincide.
• Option D: To construct an angle bisector, we use the method of folding the angle such that one side of the angle coincides with the other side (a different construction from repeated perpendiculars).

Answer:

A. a parallel to a line through a point not on the line.