Question

alex used a compass and straightedge to complete the construction below.

which statement best describes alexs construction?

a. alex constructed line cd parallel to line segment ab.
b. alex constructed line cd congruent to segment ab.
c. alex constructed line cd to be the angle divisor of segment ab.
d. alex constructed line cd to be the perpendicular bisector of segment ab.

Explanation:

Identify the construction steps shown in the diagram

The diagram shows a line segment \(AB\) with two intersecting arcs above and below it, centered at points \(A\) and \(B\) with equal radii. The line \(CD\) is drawn through these intersection points \(C\) and \(D\).

Determine the geometric property of the constructed line

The intersection points \(C\) and \(D\) are equidistant from endpoints \(A\) and \(B\), meaning \(AC = BC\) and \(AD = BD\). By definition, any line passing through points equidistant from the endpoints of a segment is the perpendicular bisector of that segment.

Match with the given options

Option D states that Alex constructed line \(CD\) to be the perpendicular bisector of segment \(AB\), which matches the identified construction.

Answer:

• A. Alex constructed line CD parallel to line segment AB.
• B. Alex constructed line CD congruent to segment AB.
• C. Alex constructed line CD to be the angle bisector of segment AB.
• D. Alex constructed line CD to be the perpendicular bisector of segment AB. (Correct answer)