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8-4

8-4. Properties of Circles. Course 2. Warm Up. Problem of the Day. Lesson Presentation. 8-4. Properties of Circles. Course 2. Insert Lesson Title Here. Objective. Learn to identify parts of a circle and to find central angle measures. Vocabulary. chord arc central angle sector.

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8-4

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  1. 8-4 Properties of Circles Course 2 Warm Up Problem of the Day Lesson Presentation

  2. 8-4 Properties of Circles Course 2 Insert Lesson Title Here Objective Learn to identify parts of a circle and to find central angle measures. Vocabulary chord arc central angle sector circle center of a circle radius diameter

  3. 8-4 Properties of Circles Course 2 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°

  4. 8-4 Properties of Circles Course 2 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.

  5. 8-4 Properties of Circles Course 2 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

  6. 8-4 Properties of Circles MN, MR, MQ, MO NR, QO NR, QO, QN, NP Reading Math Radii is the plural form of radius. Course 2 Additional Example 1: Identifying Parts of a Circle Name the parts of circle M. N A. radii: O P B. diameters: M Q C. chords: R

  7. 8-4 Properties of Circles GB, GA, GF, GD BF, AD AH, AB, CE, BF, AD Course 2 Check It Out: Example 1 Name the parts of circle M. B A C A. radii: G B. diameters: D H F E C. chords:

  8. 8-4 Properties of Circles Course 2 Sector A central angle of a circle is an angle formed by two radii. A sectorof 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

  9. 8-4 Properties of Circles Course 2 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.

  10. 8-4 Properties of Circles 1 Understand the Problem Course 2 Additional Example 2 Continued 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.

  11. 8-4 Properties of Circles Course 2 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°

  12. 8-4 Properties of Circles 3 Solve Make a Plan 2 Course 2 Additional Example 2 Continued 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° 0.40 · 360° = 144° Multiply. The central angle of the sector is 144°.

  13. 8-4 Properties of Circles 4 Course 2 Additional Example 2 Continued Look Back The 40% sector is less than half the graph, and 144° is less than half of 360°. Therefore, the answer is reasonable.

  14. 8-4 Properties of Circles Course 2 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.

  15. 8-4 Properties of Circles 1 Understand the Problem Course 2 Check It Out: Example 2 Continued 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.

  16. 8-4 Properties of Circles 3 Solve Make a Plan 2 Course 2 Check It Out: Example 2 Continued 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° 0.35 · 360° = 126° Multiply. The central angle of the sector is 126°.

  17. 8-4 Properties of Circles 4 Course 2 Check It Out: Example 2 Continued Look Back The 35% sector is less than half the graph, and 126° is less than half of 360°. Therefore, the answer is reasonable.

  18. 8-4 Properties of Circles BA, BC AC DE, FE, AC Course 2 Insert Lesson Title Here Lesson Quiz Name the parts of circle B. 1. radii 2. diameter(s) 3. chord(s) 4. A pie is cut into 8 equal sectors. Find the measure of the central angle of one slice of pie. 45°

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