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

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

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

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.

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

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

Postulate 11-1 Symbol: 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

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

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

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

Class work Practice 11-2 Show work