Arcs of Chords

Chords Connects two points on the circumference of the circle. O S U Segment SU is a chord.

Arcs of Chords The endpoints of a chord form an arc. O S U Chord SU forms arc SU.

Five Things to Remember about Arcs of Chords In the same circle or congruent circles, #1 Congruent arcs have congruent chords. O A K X T Arc AK = 80  and arc TX = 80  Since Arc AK  arc TX, then… Chord AK  chord TX. 80 

Five Things to Remember about Arcs of Chords In the same circle or congruent circles, #2 Congruent chords have congruent arc. O A K X T Chord TX = 8 and chord AK = 8 Since chord AK  chord TX, then… Arc AK  arc TX. 8 8

Five Things to Remember about Arcs of Chords #3 A diameter that is perpendicular to a chord, bisects the chord and it’s arc. O C B A F Segment BE  segment BF and… Arc CF  arc CE. E Segment CA is a diameter. Diameter CA is perpendicular to chord EF, so…

Five Things to Remember about Arcs of Chords In the same circle or congruent circles, #4 Chords with the same distance from the center are congruent. X U V T R Segment SX = 5 and segment XW = 5 Since SX  XW, then… Chord RT  chord UV  5 W S

Five Things to Remember about Arcs of Chords In the same circle or congruent circles, #5 Congruent chords are the same distance away from the center. X U V T R Chord RT = 6 and chord UV = 6. Since RT  UV, then… SX  XW. 3 3 W S 3 3