Circles: Arcs and Chords

Section 9-3: Theorems of Congruence

Circles: Theorem 9-1 • In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

D E FE  DB  FE  DB B A FE  DB  FE  DB F

Circles: Theorem 9-2 C • In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.

F E D FG is a diameter.

CD  FG  CE  ED and CF  FD A B G

Circles: Theorem 9-3 • In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

D C G

AH



AG



EF



CD

A

EF



CD



AH



AG

E H B F