1 / 56

Unit 3 Circles

Unit 3 Circles. C. Parts of a Circle. Circle – set of all points _________ from a given point called the _____ of the circle. equidistant. C. center. Symbol:. CHORD:. A segment whose endpoints are on the circle. Radius. RADIUS:. Distance from the center to point on circle. P.

tam
Télécharger la présentation

Unit 3 Circles

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 3 Circles

  2. C Parts of a Circle Circle – set of all points _________ from a given point called the _____ of the circle. equidistant C center Symbol:

  3. CHORD: A segment whose endpoints are on the circle

  4. Radius RADIUS: Distance from the center to point on circle P

  5. DIAMETER: Diameter Distance across the circle through its center P Also known as the longest chord.

  6. D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

  7. Q R P S T Use P to determine whether each statement is true or false.

  8. Secant Line: intersects the circle at exactly TWO points

  9. Tangent Line: a LINE that intersects the circle exactly ONE time Forms a 90°angle with a radius Point of Tangency: The point where the tangent intersects the circle

  10. Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

  11. Central Angle : An Angle whose vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P To name: use 3 letters C To name: use 2 letters B APB is a Central Angle

  12. EDF Semicircle: An Arc that equals 180° To name: use 3 letters E D P F

  13. THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

  14. measure of an arc = measure of central angle m AB m ACB m AE A E 96 Q = 96° B C = 264° = 84°

  15. Arc Addition Postulate m ABC = m AB + m BC A C B

  16. m DAB = Tell me the measure of the following arcs. 240 D A 140 260 m BCA = R 40 100 80 C B

  17. CONGRUENT ARCS Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45 110 A Arc length is proportional to “r”

  18. Warm up

  19. Central Angle Angle = Arc

  20. Inscribed Angle • Angle where the vertex in ON the circle

  21. Inscribed Angle

  22. 160 The arc is twice as big as the angle!! 80

  23. Find the value of x and y. 120  x  y 

  24. J K Q S M Examples 1. If mJK= 80 and JMK = 2x – 4, find x. x = 22 2. If mMKS= 56, find m MS. 112 

  25. Find the measure of DOG and DIG D 72˚ G If two inscribed angles intercept the same arc, then they are congruent. O I

  26. If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

  27. Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY B A D C

  28. If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. diameter

  29. Q D 3 J T 4 U Example 3 In J, m3 = 5x and m 4 = 2x + 9. Find the value of x. x = 3

  30. Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G Bonus: What type of triangle is this? Why?

  31. Example 5 Find y and z. z 110 110 + y =180 y y = 70 85 z + 85 = 180 z = 95

  32. Warm Up 1. Solve for arc ABC 244 2. Solve for x and y. x = 105 y = 100

  33. Wheel of Formulas!!

  34. Vertex is INSIDE the Circle NOT at the Center

  35. Ex. 1 Solve for x 88 84 X x= 100

  36. Ex. 2 Solve for x. 93 xº 45 89 x = 89

  37. Vertex is OUTside the Circle

  38. Ex. 3 Solve for x. x 15° 65° x = 25

  39. Ex. 4 Solve for x. 27° x 70° x= 16

  40. Ex. 5 Solve for x. 260° x x = 80

  41. Tune: If You’re Happy and You Know It • If the vertex is ON the circle halfthe arc. <clap, clap> • If the vertex is INside the circle half the sum. <clap, clap> • But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the differenceanyway. <clap, clap>

  42. Warm up: Solve for x 1.) 124◦ 2.) 70◦ x 18◦ x 4.) 3.) 260◦ x 20◦ 110◦ x

  43. Circumference & Arc Lengthof Circles

  44. 2 Types of Answers Rounded • Type the Pi button on your calculator • Toggle your answer • Round Exact • Type the Pi button on your calculator • Pi will be in your answer • TI 36X Pro gives exact answers

  45. Circumference The distance around a circle

  46. Circumference or

  47. r = 14 feet d = 15 miles Find the EXACT circumference.

  48. 33 yd Ex 3 and 4: Find the circumference. Round to the nearest tenth. 14.3 mm

  49. 5. A circular flower garden has a radius of 3 feet. Find the circumference of the garden to the nearest hundredths. C = 18.85 ft

  50. Arc Length The distance along the curved line making the arc (NOT a degree amount)

More Related