9-2 Angles and Arcs Objectives: To recognize major arcs, minor arcs, semicircles, and central angles. To find measures of arcs and central angles. To solve problems by making circle graphs.

Vocabulary Central Angle Similar Circles Arcs Congruent Circles Minor Arc Congruent Arcs Major Arc Semicircle Adjacent Arcs Arc Length Concentric Circles

Central Angles A central angle is an angle whose vertex is at the center of a circle.

Sum of Central Angles The sum of the measures of the central angles of a circle with no interior points in common is 360°.

Example 1 Determine the measure of each central angle used by the artist to draw the pie chart.

Arcs A central angle separates a circle into arcs. LY is a minor arc of Circle E. LUY is a major arc of Circle E.

Semicircle If the measure of a arc is 180°, it is called a semicircle. Semicircles are congruent arcs formed when the diameter of a circle separates the circle into two arcs.

Definition of Arc Measure The measure of a minor arc is the measure of its central angle. The measure of a major arc is 360° minus the measure of its central angle. The measure of a semicircle is 180°.

Postulate 9-1 Arc Addition Postulate

Arc Length Arc Length is NOT the same as the arc measure. Arc length is a distance measured in units such as centimeters. Arc Measure is measured in degrees.

Example 2

Concentric Circles Concentric Circles lie in the same plane and have the same center, but have different radii. An archery or rifle target is an excellent example. All circles are similar circles.

Congruent Circles Circles that have the same radii are congruent circles. Two arcs on the SAME circle with the same measure are congruent arcs.

Homework 9-2 Worksheet