Geometry

Geometry Arcs and Central Angles

Symbols • Circle • Arc

Goals • Identify arcs & central angles in circles • Compute arc measures and angle measures

Central Angle An angle whose vertex is the center of a circle. A

Minor Arc Part of a circle. The measure of the central angle is less than 180. C T A

Semicircle Half of a circle. The endpoints of the arc are the endpoints of a diameter. The central angle measures 180. C A T D

Major Arc Part of a circle. The measure of the central angle is greater than 180. C T A D

Major Arc C BUT NOT T A D

Measuring Arcs • An arc has the same measure as the central angle. • We say, “a central angle subtends an arc of equal measure”. A 42 42 B C

A 42 42 B C Measuring Major Arcs • The measure of an major arc is given by 360 measure of minor arc. D

R A C T Arc Addition Postulate

Q 40 R T 60 S P 120 What have you learned so far? • 1) • 2) • 3) • 4) • 5) • 6)

Homework