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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 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.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  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°

  3. California Standards MG3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

  4. Vocabulary circle center of a circle arc radius diameter chord central angle sector

  5. 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. This distance is called the radius of the 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.

  6. 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

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

  8. GB, GA, GF, GD BF, AD AH, AB, CE, BF, AD 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:

  9. 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. Sector ) 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

  10. 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.

  11. 1 Understand the Problem Additional Example 2 Continued List the important information: • The percent of people whose favorite muffin is blueberry is 40%.

  12. 3 Solve Make a Plan 2 Additional Example 2 Continued The central angle measure of the sector that represents this group is 40% of the angle measure of the whole circle. The angle measure of a circle is 360°. 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 measures 144°.

  13. 4 Additional Example 2 Continued Look Back The 40% sector is less than half the graph, and 144° is less than half of 360°. Since 144° is close to 180°, the answer is reasonable.

  14. Check It Out! Example 2 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 banana nut.

  15. 1 Understand the Problem Check It Out! Example 2 Continued List the important information: • The percent of people whose favorite muffin is banana nut is 35%.

  16. 3 Solve Make a Plan 2 Check It Out! Example 2 Continued The central angle measure of the sector that represents this group is 35% of the angle measure of the whole circle. The angle measure of a circle is 360°. Since the sector is 35% of the circle graph, the central angle measure 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 measures 126°.

  17. 4 Check It Out! Example 2 Continued Look Back The 35% sector is about one-third the graph, and 126° is about one-third of 360°. Since 126° is close to 120°, the answer is reasonable.

  18. BA, BC AC DE, FE, AC 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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