Question

name: nicoly felix period: 3 date: 15/09/2025 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. a. line cd is perpendicular to segment ab b. point m is the mid - point of segment ab c. the length ab is the equal to the length cd. d. segment am is perpendicular to segment bm e. cb + bd>cd

Explanation:

Step1: Recall straight - edge and compass construction properties

In this construction, the line \(CD\) is the perpendicular bisector of the segment \(AB\).

Step2: Analyze option A

Since \(CD\) is the perpendicular bisector of \(AB\), line \(CD\) is perpendicular to segment \(AB\). So option A is true.

Step3: Analyze option B

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

Step4: Analyze option C

There is no reason for \(AB\) to be equal to \(CD\). The lengths depend on the radii of the circles and the construction. So option C is false.

Step5: Analyze option D

\(AM\) and \(BM\) are collinear (both lie on \(AB\)), so they are not perpendicular. Option D is false.

Step6: Analyze option E

By the triangle inequality in \(\triangle CBD\), \(CB + BD>CD\). So option E is true.

Answer:

A. Line \(CD\) is perpendicular to segment \(AB\)
B. Point \(M\) is the midpoint of segment \(AB\)
E. \(CB + BD>CD\)