Question

circle d is shown with the measures of the minor arcs. which segments are congruent? (overline{ef}) and (overline{gf}) (overline{eh}) and (overline{ef}) (overline{fg}) and (overline{eh}) (gh) and (fe)

Explanation:

Step1: Recall the property of congruent chords

In a circle, if two minor arcs are congruent, then their corresponding chords are congruent.

Step2: Analyze the given arc measures

We are given that arc \(EH = 65^{\circ}\) and arc \(FG=65^{\circ}\) (since \(360-(115 + 115+65)=65^{\circ}\) for arc \(EH\) and arc \(FG\) is also \(65^{\circ}\) as per the property of congruent arcs in a circle).
Since arc \(EH\) and arc \(FG\) have the same measure (\(65^{\circ}\)), by the property that congruent arcs correspond to congruent chords, chord \(\overline{EH}\) and chord \(\overline{FG}\) are congruent.

Answer:

\(\overline{FG}\) and \(\overline{EH}\)