Section 10.2 Arcs and Chords

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Section 10.2 Arcs and Chords
*Watch this video to give you a better grasp of the concepts listed below.*
Vocabulary:
Central Angle- Angle whose vertex the center of a circle. (Any angle drawn with the vertex at the center) <ACB
*The measure of a central angle is the measure of its intercepted arc.
Minor Arc- Part of a circle that measures less than 180.
*Named: by their endpoints
*Measure: The measure of its central angle.
Major Arc- Part of a circle that measures between 180 and 360.
*Named by their endpoints and a point on the arc.
*Measure: 360- the measure of its associated minor arc.
Semicircle- Part of a circle that measures 180.
*Named by their endpoints and by a point on the arc.
Name all Central Angles
Name all Minor Arcs
Name all Major Arcs
Name all Semicircles
Congruent Arcs- Two arcs of the same circle or of congruent circles are congruent if they have the same measure.
Postulate 26: Arc Addition Postulate
The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.
Theorem 10.4
In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are
congruent.
Theorem 10.5
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
Theorem 10.6
If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.
Theorem 10.7
In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the
center.
Examples:
1. Find each measure.
a)
b)
c)
d)
2. Find
3. Find CG
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