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Agenda: 4/12/11

Agenda: 4/12/11. Warm - up Lesson 11-2: Arcs and Central Angles (p. 462) Vocabulary Examples Classwork Homework: Page 466 #’s 13 – 35 (all) Page 467 (Quiz 1) #’s 1-10 (all). Warm - up. Lesson 11-2: ARCS AND CENTRAL ANGLES. Central Angle.

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Agenda: 4/12/11

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  1. Agenda:4/12/11 Warm - up Lesson 11-2: Arcs and Central Angles (p. 462) Vocabulary Examples Classwork Homework: Page 466 #’s 13 – 35 (all) Page 467 (Quiz 1) #’s 1-10 (all)

  2. Warm - up

  3. Lesson 11-2: ARCS AND CENTRAL ANGLES

  4. Central Angle • Formed when the two sides of an angle meet at the center of the circle. P Central angle O Q Arcs – are curved lines

  5. Three Types of Arcs • Minor 2. Major 3. Semicircle P P P R R G G G W K Part of the circle in the interior of the circle in the interior of the central angle with measure less than 1800. K K Part of the circle in the exterior of the central angle. Are congruent arcs whose endpoints lie on a diameter of the circle.

  6. Three Types of Arcs • Minor 2. Major 3. Semicircle P P P R R G G G W K Part of the circle in the interior of the circle in the interior of the central angle with measure less than 1800. K K Part of the circle in the exterior of the central angle. Are congruent arcs whose endpoints lie on a diameter of the circle.

  7. Definition of Arc Measure • The degree measure of a minor arc is the degree measure of its central angle. • The degree measure of a major arc is 360 minus the degree measure of the central angle. • The degree measure of a semicircle is 180.

  8. Example #1 • In J , find mLM, m KJM, and mLK. K J 1300 1250 L M

  9. Adjacent Arcs • Have exactly one point in common Symbol: R P T S

  10. Postulate 11-1 • Arc Definition Postulate • The sum of the measure of two adjacent arcs is the measure of the arc formed by the adjacent arcs. Symbol: P Q C R

  11. Example #2 • In A, CE is a diameter. Find mBC, mBE, and mBDE. D 820 7 C E 480 A B

  12. Theorem 11-3 • In a circle or in congruent circles, two minor arcs are congruent if and only if their corresponding central angles are congruent. Symbol: A C 300 Q 300 B D

  13. Example #3 • In M, WS and RT are diameters, m WMT = 125, and mRK = 14. Find mRS and mRW. R K W M S T

  14. Class work Practice 11-2 Show work

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