12.2 chords and arcs theorem 12.4 and its converse – theorem – within a circle or in congruent...

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12.2 Chords and Arcs • Theorem 12.4 and Its Converse – Theorem – • Within a circle or in congruent circles, congruent central angles have congruent arcs. – Converse – • Within a circle or in congruent circles, congruent arcs have congruent central angles.

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Page 1: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

12.2 Chords and Arcs• Theorem 12.4 and Its Converse– Theorem – • Within a circle or in congruent circles, congruent central angles

have congruent arcs.

– Converse – • Within a circle or in congruent circles, congruent arcs have

congruent central angles.

Page 2: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.5 and Its Converse• Theorem - Within a circle or in congruent circles, congruent

central angles have congruent chords.• Converse – Within a circle or in congruent circles,

congruent chords have congruent central angles.

Page 3: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.6 and Its Converse• Theorem – Within a circle or in congruent circles,

congruent chords have congruent arcs.• Converse – Within a circle or in congruent circles,

congruent arcs have congruent chords.

Page 4: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.7 and Its Converse• Theorem – Within a circle or in congruent circles, chords

equidistant from the center or centers are congruent.• Converse – Within a circle or in congruent circles,

congruent chords are equidistant from the center (or centers.

Page 5: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.8• In a circle, if a diameter is perpendicular to a chord, then it

bisects the chord and its arc.

Page 6: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.9• In a circle, if a diameter bisects a chord (that is not a

diameter) then it is perpendicular to the chord.

Page 7: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

Theorem 12.10• In a circle, the perpendicular bisector of a chord contains

the center of the circle.

Page 8: 12.2 Chords and Arcs Theorem 12.4 and Its Converse – Theorem – Within a circle or in congruent circles, congruent central angles have congruent arcs. –

More Practice!!!!!

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