Theorem 9-4
description
Transcript of Theorem 9-4
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Theorem 9-4Theorem 9-4
•In the same circle (or congruent circles)–Congruent arcs have congruent chords.–Congruent chords have congruent arcs.
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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
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Theorem 9-5Theorem 9-5
•A diameter that is perpendicular to a chord bisects the chord and its arc.
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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
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Try this one…Try this one…• Given: • EF=10• AZ=5
• Find ZB• Find arc DB
A
B
C
D
Z
E
F€
86°
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CD⊥AB
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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.