5-Minute Check on Lesson 10-1 Transparency 10-2 Click the mouse button or press the Space Bar to display the answers. Refer to ⊙ F. 1. Name a radius 2. Name a chord 3. Name a diameter Refer to the figure and find each measure 4. BC 5. DE 6. Which segment in ⊙ C is a diameter? Standardized Test Practice: ACBD ACCDCB AB FL, FM, FN, FO LN, MO, MN, LO LN, MO 3 13 D D A C B

Lesson 10-2 Angles and Arcs

Objectives Recognize major arcs, minor arcs, semicircles, and central angles and their measures –central angles sum to 360° –major arcs measure > 180° –minor arcs measure < 180° –semi-circles measure = 180° Find arc length –Formula: C (central angle / 360°) % of circle that is the arc

Vocabulary Central Angle – has the center of the circle as its vertex and two radii as sides Arc – edge of the circle defined by a central angle Minor Arc – an arc with the central angle less than 180° in measurement Major Arc – an arc with the central angle greater than 180° in measurement Semicircle – an arc with the central angle equal to 180° in measurement Arc Length – part of the circumference of the circle corresponding to the arc

Circles - Arcs y x Central Angle Diameter (d) Center B G F E H BHG BEG Semi-Circle EHF

Circles - Probability y x Radius (r) Diameter (d) Center Circumference = 2 πr = dπ 0° 180° 90° 270° 135° 315° Pie Charts Probability 0 = no chance 1 = for sure 135º = 3/8 360º or.375 or 37.5% 180º = 1/2 360º or.5 or 50% 45º = 1/8 360º or.125 or 12.5%

Example 2-1a Find. EXAMPLE 1

Example 2-1b Substitution Simplify. Add 2 to each side. Divide each side by 26. Use the value of x to find Given Substitution Answer: 52 The sum of the measures of (CONT)

Example 2-1c ALGEBRA Refer to. Find. EXAMPLE 2

Linear pairs are supplementary. Substitution Simplify. Subtract 140 from each side. form a linear pair. Answer: 40 (CONT)

Example 2-1e Answer: 65 Answer: 40 ALGEBRA AD and BE are diameters a. Find m b. Find m EXAMPLE 3

Example 2-2a Find. In bisects and is a minor arc, so is a semicircle. Answer: 90 EXAMPLE 4

Example 2-2c Find. In bisects and since bisects. is a semicircle. Answer: 67 EXAMPLE 5

Example 2-2e Find. In bisects and Answer: 316 EXAMPLE 6

Example 2-2g Answer: 54 Answer: 72 In and are diameters, and bisects Find each measure. a. b. c. Answer: 234 EXAMPLE 7

Example 2-4a In and. a) Find the length of. b) Find the length of arc DC. In and. Write a proportion to compare each part to its whole. degree measure of arc degree measure of whole circle arc length circumference EXAMPLE 8

Example 2-4b Now solve the proportion for. Simplify. Answer: The length of is units or about 3.14 units. Multiply each side by 9. Answer: The length of arc DC is 7 π/2 units or about 11 units. C ∙ (% of the circle) = 9π ∙ (140/360) = 7π/2 (CONT)

Summary & Homework Summary: –Sum of measures of central angles of a circle with no interior points in common is 360° –Measure of each arc is related to the measure of its central angle –Length of an arc is proportional to the length of the circumference Homework: –pg ; 14-23; 24-29; 32-35