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 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

5. Three Types of Arcs 2. Major Minor 3. SemicircleK 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.

6. Three Types of Arcs 2. Major Minor 3. SemicircleK 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.

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 L
1250 M

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

10. 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

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