1 / 11

UNIT 5

UNIT 5. Circles. Key Term (only write what’s in RED ). Circle: the set of a all points that are a given distance from a given point called the center KEEP IN MIND:

sasha
Download Presentation

UNIT 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. UNIT 5 Circles

  2. Key Term (only write what’s in RED) • Circle: the set of a all points that are a given distance from a given point called the center KEEP IN MIND: A circle is a shape with all points the same distance from its center. A circle is named by its center. Thus, the circle below is called circle A since its center is at point A. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin. written as: A (circle A)

  3. Key Terms Do you remember…? • Arc: part of the circumference of a circle • Semicircle: half of a circle (180°) • Minor Arc: smaller than a semicircle (2 letters) • Major Arc: greater than a semicircle (3 letters)

  4. Identify: • Semicircles  ________________________________ • Minor Arcs  ________________________________ • Major Arcs  ________________________________ B C E BONUS What’s the name of the circle?? A D

  5. *the measure of an arc is EQUAL to the measure of its CENTRAL ANGLE

  6. EX. 1a) Find the measure of each arc in Q. mCD: 40° mAD: 180° - 40° = 140° mCAD: 360° - 40° = 320° or 140° + 180° = 320° mDCA: 360° - 140° = 220° or 180° + 40° = 220° D 40° A C Q

  7. EX. 1 (YOU TRY)B) Find the measure of each arc in Q. B mDC: ___________ mEB: ___________ mDAC: ___________ mACD: ___________ Q C A 35° 75° E D

  8. Parts of a Circle KEEP IN MIND: The distance across a circle through the center is called the diameter. A real-world example of diameter is a 9-inch plate. The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. A chord (pronounce CORD) is a line segment that joins two points on a curve. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. The circle to the top right contains chord AB.

  9. CIRCLE FORMULAS CIRCUMFERENCE AREA • C = πd or • C = 2πr Why are these equations the same?? • A = πr×r or • A = πr2 Why are these equations the same??

  10. Ex. 2Find the circumference and area of each .(Fill in the blanks) 2.3 cm 15m 3 in. 5 in. C = πd C = π(15) C = 47.1 m A = πr2 A = π(7.5)2 A = 176. 7 m2 *hint: use PT C = πd C = π( ____ ) C = _____cm A = πr2 A = π(2.3)2 A = 16.6 cm2 C = πd C = π( ____ ) C = _____ in. A = πr2 A = π( ____ )2 A = _______in2

  11. Ex. 3) The diameter of a bicycle wheel is 17 inches. If the wheel makes 10,500 revolutions, how far did the bike travel? d = 17; C = πd C = π(17) C ≈ 53.4 For 1 revolution, the bike traveled about 53.4 in. To find the distance traveled for 10,500 revolutions, multiply: C ≈ 53.4 × 10,500 C ≈ 560,774.3 inches

More Related