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Geometry Insights: Exploring Arcs and Angles in Circles

It's Friday! Today, we're diving into the fascinating world of geometry with a focus on arcs and angles. Megan is incorporating an equilateral triangle into her sweatshirt design, where each side measures 12 inches. We’ll explore the properties of circles, including vertex relationships and angle measures. With example problems to clarify concepts, you’ll learn how to determine the length of various lines connecting points within circles. Join us for a fun mathematical exploration that enhances your geometry knowledge!

lamar-atkinson
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Geometry Insights: Exploring Arcs and Angles in Circles

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Presentation Transcript

  1. It’s Friday!!! September 6, 2013 Daily Check: Naming Arcs & Central Angles

  2. Megan is using an equilateral triangle as part of a design on a sweatshirt. Each side of the triangle is 12 inches long. Megan is gluing a line of stars from the midpoint of one side of this triangle to the opposite vertex. Approximately how long will the line of stars be? EOCT Review • 13.4 • 10.4 • 8.5 • 5.2 b

  3. CCGPS Geometry UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: What other angle relationships do we know for circles? Standard: MMC9-12.G.C.2

  4. Case I:Vertex is AT the center A P C B

  5. Case II:Vertex is ON circle ANGLE ARC ARC ANGLE

  6. Ex. 1 Find m1. 1 84° m<1 = 42

  7. 202° Ex. 2 Find m1. 1 m<1 = 79

  8. Case III:Vertex is INSIDE circle A ARC B ANGLE D ARC C Looks like a PLUS sign!

  9. Ex. 3 Find m1. 93° A B 1 D C 113° m<1 = 103

  10. Ex. 4 Find mQT. mQT = 100 N Q 84 92 M T

  11. Ex. 5 Find x. 93 xº 45 89 x = 89

  12. Case IV:Vertex is OUTSIDE circle C ANGLE small ARC A D LARGE ARC B

  13. Ex. 6 Find m1. 1 15° A D 65° B m<1 = 25

  14. Ex. 7 Find mAB. mAB = 16 A 27° 70° B

  15. Ex. 8 Find m1. 260° 1 m<1 = 80

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