Theorem 9-4Theorem 9-4

•In the same circle (or congruent circles)–Congruent arcs have congruent chords.–Congruent chords have congruent arcs.

ExampleExample• If arc AB is congruent to arc BC, then segment AB is congruent to segment BC

• The converse is true also…

A

B C

D

Theorem 9-5Theorem 9-5

•A diameter that is perpendicular to a chord bisects the chord and its arc.

ExampleExample• If CD is perpendicular to AB, then – AZ is cong to BZ– Arc AD is cong to Arc BD

A

B

C

D

Z

Try this one…Try this one…• Given: • EF=10• AZ=5

• Find ZB• Find arc DB

A

B

C

D

Z

E

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CD⊥AB

Theorem 9-6Theorem 9-6

•In the same circle (or in congruent circles)–Chords equally distant from the center are congruent.–Congruent chords are equally distant from the center.