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CCGPS Geometry Day 20 (9-4-13)

CCGPS Geometry Day 20 (9-4-13). 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: How do we use angle measures to find measures of arcs? Standard: MMC9-12.G.C.2. AGENDA. Notes on Circles

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CCGPS Geometry Day 20 (9-4-13)

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  1. CCGPS GeometryDay 20 (9-4-13) 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: How do we use angle measures to find measures of arcs? Standard: MMC9-12.G.C.2

  2. AGENDA • Notes on Circles • Notes on Central Angles • Practice Worksheet • Homework Worksheet

  3. Unit 3 Circles

  4. Segments of Circles

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

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

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

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

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

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

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

  12. 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

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

  14. Central Section 6.2 Arcs

  15. 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

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

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

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

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

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

  21. 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”

  22. Classwork • Practice Worksheet

  23. Homework: • Practice Worksheet

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