Question

click the arrows to choose an answer from each menu. $overline{ac}congoverline{ab}$ because all choose... are congruent. $overline{ab}congoverline{bc}$ because all choose... are congruent. choose... by the transitive property. $\triangle abc$ is an equilateral triangle because choose... sides are congruent.

Explanation:

Step1: Recall circle - radius property

In the first circle with center \(A\), \(\overline{AC}\) and \(\overline{AB}\) are radii of the circle centered at \(A\). Since all radii of a circle are congruent, \(\overline{AC}\cong\overline{AB}\).

Step2: Recall circle - radius property

In the second circle with center \(B\), \(\overline{AB}\) and \(\overline{BC}\) are radii of the circle centered at \(B\). Since all radii of a circle are congruent, \(\overline{AB}\cong\overline{BC}\).

Step3: Apply transitive property

If \(a = b\) and \(b = c\), then \(a = c\). Here, since \(\overline{AC}\cong\overline{AB}\) and \(\overline{AB}\cong\overline{BC}\), by the transitive property of congruence, \(\overline{AC}\cong\overline{BC}\).

Step4: Recall equilateral - triangle definition

An equilateral triangle is a triangle with all three sides congruent. Since \(\overline{AC}\cong\overline{AB}\), \(\overline{AB}\cong\overline{BC}\) and \(\overline{AC}\cong\overline{BC}\), \(\triangle ABC\) is an equilateral triangle because all three sides are congruent.

Answer:

1. Radii of a circle
2. Radii of a circle
3. \(\overline{AC}\cong\overline{BC}\)
4. all three