8-4 Properties of Circles Warm Up Problem of the Day Course 2 Warm Up Problem of the Day Lesson Presentation

8-4 Properties of Circles Warm Up Course 2 8-4 Properties of Circles Warm Up 1. Two angles are supplementary. One angle measures 61°. Find the measure of the other angle. 2. Two angles are complementary. One angle measures 19°. Find the measure of the other angle. 3. Two angles are supplementary and congruent. Find the measure of each angle. 119° 71° 90°

8-4 Properties of Circles Problem of the Day Course 2 8-4 Properties of Circles Problem of the Day In a circle graph, three sectors representing 15%, 25%, and 30% are labeled. What percent does the fourth sector represent, and what is its measure in degrees? 30%; 108°

8-4 Properties of Circles Course 2 8-4 Properties of Circles Learn to identify parts of a circle and to find central angle measures.

Insert Lesson Title Here Course 2 8-4 Properties of Circles Insert Lesson Title Here Vocabulary circle center of a circle radius diameter chord arc central angle sector

8-4 Properties of Circles Course 2 8-4 Properties of Circles A circle is the set of all points in a plane that are the same distance from a given point, called the center of a circle. A circle is named by its center. For example, if point A is the center of a circle, then the name of the circle is circle A. There are special names for the different parts of a circle.

8-4 Properties of Circles Diameter Arc Course 2 8-4 Properties of Circles Diameter Arc Part of a circle named by its endpoints Line segment that passes through the center of a circle, and whose endpoints lie on the circle Radius Line segment whose endpoints are the center of a circle and any point on the circle Chord Line segment whose endpoints are any two points on a circle

Additional Example 1: Identifying Parts of a Circle Course 2 8-4 Properties of Circles Additional Example 1: Identifying Parts of a Circle Name the parts of circle M. N A. radii: MN, MR, MQ, MO O P B. diameters: NR, QO M Q C. chords: NR, QO, QN, NP R Radii is the plural form of radius. Reading Math

8-4 Properties of Circles Check It Out: Example 1 Course 2 8-4 Properties of Circles Check It Out: Example 1 Name the parts of circle M. B A C A. radii: GB, GA, GF, GD G B. diameters: BF, AD D H F C. chords: AH, AB, CE, BF, AD E

8-4 Properties of Circles A central angle of a circle Course 2 8-4 Properties of Circles Sector A central angle of a circle is an angle formed by two radii. A sector of a circle is the part of the circle enclosed by two radii and an arc connecting them. ) The sum of the measures of all of the central angles in a circle is 360°. We say that there are 360° in a circle. Central angle

8-4 Properties of Circles Course 2 8-4 Properties of Circles Additional Example 2: Problem Solving Application The circle graph shows the results of a survey about favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is blueberry.

Understand the Problem Course 2 8-4 Properties of Circles Additional Example 2 Continued 1 Understand the Problem The answer is the measure of the central angle that represents blueberry. List the important information: • The percent of people whose favorite muffin is blueberry is 40%. • The central angle measure of the sector that represents this group is 40% of the 360° of the circle.

Additional Example 2 Continued Course 2 8-4 Properties of Circles Additional Example 2 Continued 2 Make a Plan There are 360° in a circle. Since the sector is 40% of the circle graph, the central angle is 40% of the 360° in the circle. 40% of 360° = 0.40 · 360° Solve 3 0.40 · 360° = 144° Multiply. The central angle of the sector is 144°.

Additional Example 2 Continued Course 2 8-4 Properties of Circles Additional Example 2 Continued 4 Look Back The 40% sector is less than half the graph, and 144° is less than half of 360°. Therefore, the answer is reasonable.

8-4 Properties of Circles Check It Out: Example 2 Course 2 8-4 Properties of Circles Check It Out: Example 2 The circle graph shows the results of a survey about the favorite types of muffins. Find the central angle measure of the sector that shows the percent of people whose favorite type of muffin is banana nut.

Understand the Problem Course 2 8-4 Properties of Circles Check It Out: Example 2 Continued 1 Understand the Problem The answer is the measure of the central angle that represents banana nut. List the important information: • The percent of people whose favorite muffin is banana nut is 35%. • The central angle measure of the sector that represents this group is 35% of the 360° of the circle.

Check It Out: Example 2 Continued Course 2 8-4 Properties of Circles Check It Out: Example 2 Continued 2 Make a Plan There are 360° in a circle. Since the sector is 35% of the circle graph, the central angle is 35% of the 360° in the circle. 35% of 360° = 0.35 · 360° Solve 3 0.35 · 360° = 126° Multiply. The central angle of the sector is 126°.

Check It Out: Example 2 Continued Course 2 8-4 Properties of Circles Check It Out: Example 2 Continued 4 Look Back The 35% sector is less than half the graph, and 126° is less than half of 360°. Therefore, the answer is reasonable.

Insert Lesson Title Here Course 2 8-4 Properties of Circles Insert Lesson Title Here Lesson Quiz Name the parts of circle B. 1. radii 2. diameter(s) 3. chord(s) 4. BA, BC AC DE, FE, AC A pie is cut into 8 equal sectors. Find the measure of the central angle of one slice of pie. 45°