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 congruent to segment BC

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


Example1

If CD is perpendicular to AB, then congruent to segment BC

AZ is cong to BZ

Arc AD is cong to Arc BD

Example

A

D

Z

B

C


Try this one

Given: congruent to segment BC

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 congruent to segment BC

  • 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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