Question

1. this diagram is a straightedge and compass construction. a is the center of one circle, and b is the center of the other. select all the true statements.

line cd is perpendicular to segment ab
point m is the midpoint of segment ab

Explanation:

Step1: Recall straight - edge and compass construction properties

In a straight - edge and compass construction of two intersecting circles with centers \(A\) and \(B\), the line joining the intersection points of the two circles (\(CD\)) is the perpendicular bisector of the line segment joining the centers (\(AB\)).

Step2: Analyze the first statement

Since the line \(CD\) is the perpendicular bisector of \(AB\), by the definition of a perpendicular bisector, line \(CD\) is perpendicular to segment \(AB\).

Step3: Analyze the second statement

As \(CD\) is the perpendicular bisector of \(AB\), the point \(M\) (the intersection of \(CD\) and \(AB\)) is the mid - point of segment \(AB\).

Answer:

Line \(CD\) is perpendicular to segment \(AB\) (True), Point \(M\) is the midpoint of segment \(AB\) (True)