Question

go and ho are congruent which means chords df and ik are also congruent. the diameter ej is perpendicular so it creates a gf must also be ________ to hk
word bank:
similar radius congruent parallel bisector congruent chords congruent
blank 1: congruent
blank 2: chords
blank 3: congruent
blank 4:
blank 5:

Explanation:

Step1: Recall chord - distance from center relationship

In a circle, if two chords are equidistant from the center, then the chords are congruent. Since \(GO = HO\) (given as congruent), and \(EJ\) is perpendicular to both \(DF\) and \(IK\) (so \(GO\) and \(HO\) are the distances from the center \(O\) to the chords \(DF\) and \(IK\) respectively), by the chord - distance from center theorem, \(DF\cong IK\). Also, \(GF\) and \(HK\) are parts of these congruent chords. If we consider the segments of the chords that are on one side of the perpendicular diameter \(EJ\), since the whole chords \(DF\) and \(IK\) are congruent and the diameters bisect the chords (perpendicular from the center to a chord bisects the chord), \(GF\) must be congruent to \(HK\).

Answer:

Blank 4: congruent