Chapter 7 Lesson 6

Chapter 7 Lesson 6 Objective: To find the measures of central angles and arcs.

Central Angles and Arcs • In a plane, a circle is the set of all points. • The set of all points equidistant from a given point is the center. • A radius is a segment that has one endpoint at the center and the other endpoint on the circle. • A diameter is a segment that contains the center of a circle and has both endpoints on the circle.

Congruent Circles have congruent radii. 5 m 5 m Central Angle is an angle whose vertex is the center of the circle. A D C B

Example 1 Finding Central Angles **Remember a circle measures 360°.** Sleep: 31% of 360 .31•360=111.6 Food: 9% of 360 .09•360=32.4 Work: 20% of 360 .20•360=72 Must Do: 7% of 360 .07•360=25.2 Entertainment: 18% of 360 .18•360=64.8 Other: 15% of 360 .15•360=54

An arc is a part of a circle. • Types of arcs • Semicircle is half of a circle. • A DAE Minor arc Major arc AB ADB • A minor arc is smaller than a semicircle. • A major arc is greater than a semicircle. • D

Identify the following in O. C A • O E D Example 2:Identifying Arcs • the minor arcs • the semicircles • 3. the major arcs that contain point A

Example 3:Identifying Arcs Identify the minor arcs, major arcs and semicircles in O with point A as an endpoint. • D • A • • minor arcs • AD, AE O • • B E • major arcs • ADE, AED • semicircles • ADB, AEB

Adjacent arcs are arcs of the same circle that have exactly one point in common. Postulate 7-1: Arc Addition Postulate The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs. mABC = mAB + mBC • • C B • A

Example 4:Finding the Measures of Arcs Find the measure of each arc. • BC 58° D C • BD B 32° • O • ABC A • AB ABC is a semicircle.

Example 5:Finding the Measures of Arcs Find mXY and mDXM in C. M mXY = mXD + mDY mXY = 40 + 56 = 96 Y W C 56° mDXM = mDX + 180 D 40° mDXM = 40 + 180 X mDXM = 220

Assignment pg.389-392 #1-26; 40-54

Chapter 7 Lesson 6