Question

2 in the construction, a is the center of one circle, and b is the center of the other. identify all segments that have the same length as segment ab. a segment ac b segment ae c segment bc d segment cd e segment de geometry·unit 1·section a·lesson 2

Explanation:

Step1: Recall the property of radius

In a circle, all radii are equal. Since \(A\) is the center of one circle, \(AC = AE=AB\) (radii of the same circle). Since \(B\) is the center of the other circle, \(BC = BD = AB\) (radii of the same circle).

Step2: Analyze \(\triangle CAB\) and \(\triangle DAB\)

\(\triangle CAB\) and \(\triangle DAB\) are equilateral triangles. The circles centered at \(A\) and \(B\) have the same radius (\(AB\)). The intersection points \(C\) and \(D\) form equilateral triangles. But \(CD
eq AB\) and \(DE
eq AB\) (by geometric construction and side - length comparison in the figure).

Answer:

A. segment \(AC\), B. segment \(AE\), C. segment \(BC\)