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 • Arcs • Minor Arc • Major Arc • Semicircle • Measure of Arcs • Arc Length • Concentric Circles • Similar Circles • Congruent Circles • Congruent Arcs

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 .