Circle Terms.notebook March 27, 2017
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- Derick Phelps
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1 notebook March 27, 2017 Welcome back! It's so good to see you! New seats today. Check the seating chart on the front chair. Do not move the desks as they are supposed to be in pods. In your groups Introduce yourself 2. Let's roll the dice! Sum of... Talk about... 2 Favorite Color 3 Favorite Place 4 Favorite Food 5 Favorite Season 6 Favorite Sport 7 Favorite Class (this semester) 8 Favorite Book 9 Favorite Animal 10 Favorite Restaurant 11 Favorite Phone App 12 Favorite Song/Artist Is the blue circle congruent, similar or both to the red circle? 3 6 Classify as Always, Sometimes or Never: ALL circles are. Similar: A S N Congruent: A S N
2 notebook March 27, 2017 Learning Objectives Circles I can define and label circle terminology: center, radius, diameter, chord, central angle, secant line, tangent line, major and minor arc, point of tangency, inscribed angles, semicircle, concentric circles I can solve problems involving radius, diameter, and circumference. Circle The set of all points in a plane at a given distant from a point. Radius A segment from a point on a circle or sphere to the center. Center Center of circle, usually O.
3 notebook March 27, 2017 Chord of a circle A line segment whose endpoints lie on a circle. C A Chord O B Diameter A chord that passes through the center of a circle. Center Diameter D Secant A line that contains a chord Tangent A line that lies in the plane of a circle and that intersects the circle at exactly one point. Point of tangency Point where the tangent line intersects the circle. E H Secant Tangent F G
4 notebook March 27, 2017 Congruent Circles Circles with the same radius. Concentric Circles Circles with the same center. Arc of a circle Two points on a circle and the continuous part of the circle between two points. Semicircle An arc that makes up half of the circle. Example: ABC D Minor arc An arc that is smaller than a semicircle. Example: AD Major arc An arc that is larger than a semicircle. Example: ACD M A C K L B
5 notebook March 27, 2017 From the Circle below, properly identify: M Two Minor arcs: K L Major arc: Semicircle: E A Arc D Minor Arc C B O. A. O B Semicircle C Major Arc Inscribed angle An angle whose vertex lies on a circle and whose sides contain chords of the circle. Central Angle Central angle An angle whose vertex is the center of a circle and whose sides are radii of the circle. Inscribed Angle
6 notebook March 27, 2017 Now, let's try to label all parts of a circle. A B J I O H G F E K radius: diameter: chord: secant: tangent: point of tangency: Major arc: Minor arc: semicircle: center: inscribed angle: central angle: C D L
7 notebook March 27, 2017 A B J I O H G F E K radius: OG diameter: JD chord: CE secant: IF tangent: LK point of tangency: D Major arc: DEA Minor arc: DE semicircle: JHD center: O inscribed angle: ABH central angle: JOG C D L A B J I O H G F E K radius: OG diameter: JD chord: CE secant: IF tangent: LK point of tangency: D Major arc: DEA Minor arc: DE semicircle: JHD center: O inscribed angle: ABH central angle: JOG C D What is the difference between JHD and JD? L
8 notebook March 27, 2017 Write an equation for the circumference of a circle in terms of the diameter, D and radius, r. C = C = Write an equation for the circumference of a circle in terms of the diameter, D and radius, r. C = πd C = 2πr
9 notebook March 27, 2017 What is the circumference of this circle? Answer in terms of π 4 cm Answer as a decimal. What is the circumference of this circle? 4 cm Answer in terms of π Answer as a decimal.
10 notebook March 27, 2017 What is the circumference of this circle? 4 cm Answer in terms of π C = 8π cm Answer as a decimal. What is the circumference of this circle? 4 cm Answer in terms of π C = 8π cm Answer as a decimal. C = cm
11 notebook March 27, 2017 If a circle has a circumference of 20π, find the radius of the circle. If a circle has a circumference of 20π ft, find the radius of the circle. C = 20π
12 notebook March 27, 2017 If a circle has a circumference of 20π ft, find the radius of the circle. C = 20π 2πr = 20π If a circle has a circumference of 20π ft, find the radius of the circle. C = 20π 2πr = 20π r = 10 ft
13 notebook March 27, 2017 If the circumference of a circle is 7π cm, find the radius. If the circumference of a circle is 7π cm, find the radius. C = 7π
14 notebook March 27, 2017 If the circumference of a circle is 7π cm, find the radius. C = 7π 2πr = 7π If the circumference of a circle is 7π cm, find the radius. C = 7π 2πr = 7π r = 3.5 cm
15 notebook March 27, 2017 If the circumference of a circle is 50 ft, find the radius. If the circumference of a circle is 50 ft, find the radius. C = 50
16 notebook March 27, 2017 If the circumference of a circle is 50 ft, find the radius. C = 50 2πr = 50 If the circumference of a circle is 50 ft, find the radius. C = 50 2πr = 50 r = 25 ft
17 notebook March 27, 2017 At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? c. How many revolutions of each wheel will it take to travel 100 feet? At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire Little tire c. How many revolutions of each wheel will it take to travel 100 feet?
18 notebook March 27, 2017 At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire C= 52(3.14) Little tire C= 18(3.14) c. How many revolutions of each wheel will it take to travel 100 feet? At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire C= 52(3.14) C= inches Little tire C= 18(3.14) C= inches c. How many revolutions of each wheel will it take to travel 100 feet?
19 notebook March 27, 2017 At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire C= 52(3.14) C= inches Little tire C= 18(3.14) C= inches c. How many revolutions of each wheel will it take to travel 100 feet? 100 ft = 1200 inches At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire Little tire C= 18(3.14) C= inches c. How many revolutions of each wheel will it take to travel 100 feet? Big tire 1200 in 100 ft = 1200 inches in C= 52(3.14) C= inches Little tire 1200 in in
20 notebook March 27, 2017 At right is a picture of a high wheeler bicycle. The diameter of the front tire is 52 inches and the rear tire is 18 inches. a. What is the circumference of each tire? Big tire Little tire C= 18(3.14) C= inches c. How many revolutions of each wheel will it take to travel 100 feet? Big tire 1200 in 100 ft = 1200 inches in C= 52(3.14) C= inches Little tire 1200 in =7.35 = in Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? (Think about the units given v. needed) Rate Your Understanding (0-5)
21 notebook March 27, 2017 Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? Rate Your Understanding (0-5) Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? C= 60(3.14) Rate Your Understanding (0-5)
22 notebook March 27, 2017 Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? C= 60(3.14) C= cm Rate Your Understanding (0-5) Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? 70,000 km = 7,000,000,000 cm C= 60(3.14) C= cm Rate Your Understanding (0-5)
23 notebook March 27, 2017 Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? 70,000 km = 7,000,000,000 cm C= 60(3.14) C= cm 7,000,000, Rate Your Understanding (0-5) Success Criteria The diameter of a sports car tire is approximately 60 cm. The warranty is good for 70,000 km. About how many revolutions will the tire make in traveling 70,000 km? 70,000 km = 7,000,000,000 cm C= 60(3.14) C= cm 7,000,000,000 =37,135,278.5 rev Rate Your Understanding (0-5)
24 notebook March 27, 2017 Homework Announcements:
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