Question

based on the given diagram, complete the sentence below.

point d is △abcs circumcenter. \\(\overline{de}\\), \\(\overline{df}\\), and \\(\overline{dg}\\) are all dropdown with options: altitudes, medians, angle bisectors, perpendicular bisectors.

Explanation:

Step1: Recall the definition of circumcenter

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle.

Step2: Analyze the given segments

Since \(D\) is the circumcenter of \(\triangle ABC\), the segments \(DE\), \(DF\), and \(DG\) which connect the circumcenter \(D\) to the sides of the triangle must be the perpendicular bisectors.

Answer:

perpendicular bisectors