11-2 Chords and Arcs  Theorems: 11-4, 11-5, 11-6, 11-7, 11-8  Vocabulary: Chord.

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Presentation transcript:

11-2 Chords and Arcs  Theorems: 11-4, 11-5, 11-6, 11-7, 11-8  Vocabulary: Chord

Vocabulary  Chord  A segment whose endpoints are on a circle. P O Q

Theorem 11-4  Within a circle or in a congruent circles: 1. Congruent central angles have congruent chords. 2. Congruent chords have congruent arcs. 3. Congruent arcs have congruent central angles.

B O #1 Using Theorem 11-4 C F D P

Theorem 11-5  Within a circle or in a congruent circles: 1. Chords equidistant from the center are congruent. 2. Congruent chords are equidistant from the center.

#2 Using Theorem 11-5 x 18

Theorem 11-6  In a circle, a diameter that is perpendicular to a chord bisects the chord and its arcs.

Theorem 11-7  In a circle, a diameter that bisects a chord (that is not a diameter) is perpendicular to the chord.

Theorem 11-8  In a circle, the perpendicular bisector of a chord contains the center of the circle.

#3 Using Diameters and Chords xy