Arcs and Central Angles Lesson 9.3 Geometry Honors

1. Arcs and Central AnglesLesson 9.3Geometry Honors Objective

2. Lesson Focus A part of a circle is called an arc. Arcs can be associated with angles whose vertices are at the center of circles. The purpose of this lesson is to study arcs and central angles.

9. Arcs and Central Angles central angle an angle with its vertex at the center of the circle minor arc the smaller of the arcs created by a central angle major arc the larger of the arcs created by a central angle semicircle The two arcs that are cut off by a diameter.

10. Arcs and Central Angles measure of a minor arc the measure of the central angle of a minor arc measure of a major arc the measure of the central angle of a major arc measure of a semicircle the measure of a semicircle is 180

11. Arcs and Central Angles adjacent arcs arcs of a circle that have exactly one point in common congruent arcs arcs in the same circle or in congruent circles that have equal measures

12. Arcs and Central Angles Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs.

13. Arcs and Central Angles Theorem In the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

14. Written Exercises Problem Set 9.3A, p.341: # 2 - 20 (even)