This document discusses angles and arcs in circles. It defines central angles as angles with the center of the circle as the vertex and radii as the sides. The measurement of an arc is equal to the measurement of its central angle. Arcs are classified as minor, semi-circle, or major depending on whether their central angle measures less than, equal to, or greater than 180 degrees, respectively. The document also provides examples of calculating arc measures and lengths using proportions relating the degree measure of the central angle to the arc length and circumference. There are homework problems assigned from the textbook.

1. SECTION 10.2
Angles and Arcs

2. ANGLE AND ARCS
 What are the major arcs, minor arcs, semicircles
and central angles and their measures?

3. CENTRAL ANGLE
 Central Angle: An angle with the center of the circle
as the vertex and radii as the sides.

4. CENTRAL ANGLE
 Sum of Central Angles =

5. CENTRAL ANGLE


6. TYPES OF ARCS
 Measurement of an Arc = Measurement of the
central Angle
 Minor: < 180°
 Semi-circle: = 180°
 Major: > 180°

7. EXAMPLE


8. EXAMPLE


9. EXAMPLE


10. HOMEWORK
 Page 533
 14 - 31

11. ANGLE AND ARCS
 How can I calculate arc measure?
 How can I calculate arc length?

12. EXAMPLE
 Find the measure of each central angle.

13. ARC LENGTH
 Another way to measure an arc
 A fraction of the circumference
 Proportion:
Degree measure
of central angle Arc length
Degrees in a circle Circumference
of a circle

14. EXAMPLE


15. EXAMPLE


16. HOMEWORK
 Page 533
 32 - 52

17. LESSON PLAN
 Intro
 Splitting a circle in pieces of pie.
 Standards-
 Supplies – slides, whiteboard, note sheets
 Timing: Two days with notes and homework. A third day will
be review and a fourth with a quiz.
 Day 1:
 Essential Questions- slides 2
 Input-slides 3-6
 Guided Practice - slides 7, 8, and 9
 Independent Practice – Book Work
 Day 2:
 Essential Questions- slides 11
 Input-slides 13
 Guided Practice - slides 12 and 14 and 15
 Independent Practice – Book Work