Question

1. the diagram to the right was constructed with a compass, straight - edge, and pencil. a, c, and e are each the center of a circle, and c is the center of the other circle. select all the true statements.

a) $overline{ab}congoverline{ad}$
b) $overline{ac}congoverline{ad}$
c) $overline{eb}congoverline{ed}$
d) $overline{ac}congoverline{ce}$
e) $overline{eb}congoverline{ec}$

Explanation:

Step1: Recall circle - radius property

In a circle, all radii are congruent.

Step2: Analyze segments related to circle A

For circle A with center A, \(AB\) and \(AD\) are radii of circle A. So, \(\overline{AB}\cong\overline{AD}\).

Step3: Analyze segments related to circle A and other circles

\(AC\) is a radius of circle A and \(AD\) is a radius of circle A, so \(\overline{AC}\cong\overline{AD}\). Also, \(AC\) is a radius of circle A and \(CE\) is a radius of circle E. Since the circles are constructed in a way that \(AC = CE\) (by the nature of the construction where the circles intersect and share common - length segments), \(\overline{AC}\cong\overline{CE}\).

Step4: Analyze segments related to circle E

For circle E with center E, \(EB\) and \(ED\) are radii of circle E, so \(\overline{EB}\cong\overline{ED}\), and \(EB\) and \(EC\) are radii of circle E, so \(\overline{EB}\cong\overline{EC}\).

Answer:

A. \(\overline{AB}\cong\overline{AD}\)
B. \(\overline{AC}\cong\overline{AD}\)
C. \(\overline{EB}\cong\overline{ED}\)
D. \(\overline{AC}\cong\overline{CE}\)
E. \(\overline{EB}\cong\overline{EC}\)