Question

1. the diagram was constructed with straightedge and compass tools. points a, b, c, d, and e are all on line segment cd. name a line segment that is half the length of cd. explain how you know.

Explanation:

Step1: Observe the construction

Since the circles are constructed with straight - edge and compass, and they are of equal radius. Let the radius of each circle be \(r\). The length of \(CD\) is composed of 4 equal - length segments (the radii of the circles).

Step2: Determine half - length segment

If \(CD\) is composed of 4 equal segments of length \(r\), then a segment that is half the length of \(CD\) will be composed of 2 equal segments of length \(r\). Looking at the line segment \(CD\), segment \(AC\) (or \(AD\), \(BE\), \(BC\) etc.) is composed of 2 radii of the circles. So, \(AC=\frac{1}{2}CD\).

Answer:

\(AC\) (or any segment like \(AD\), \(BC\), \(BE\) which is composed of two radii of the equal - sized circles)