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Theorem 9-4

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Theorem 9-4. In the same circle (or congruent circles) Congruent arcs have congruent chords. Congruent chords have congruent arcs. If arc AB is congruent to arc BC, then segment AB is congruent to segment BC The converse is true also…. Example. A. B. C. D. Theorem 9-5.

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theorem 9 4
Theorem 9-4
  • In the same circle (or congruent circles)
    • Congruent arcs have congruent chords.
    • Congruent chords have congruent arcs.
example
If arc AB is congruent to arc BC, then segment AB is congruent to segment BC

The converse is true also…

Example

A

B

C

D

theorem 9 5
Theorem 9-5
  • A diameter that is perpendicular to a chord bisects the chord and its arc.
example1
If CD is perpendicular to AB, then

AZ is cong to BZ

Arc AD is cong to Arc BD

Example

A

D

Z

B

C

try this one
Given:

EF=10

AZ=5

Find ZB

Find arc DB

Try this one…

A

D

E

Z

B

C

F

theorem 9 6
Theorem 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.
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