goemetry/notes 10.2

SECTION 10.2Angles and Arcs

ANGLE AND ARCS

What are the major arcs, minor arcs, semicircles and central angles and their measures?

CENTRAL ANGLE

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

CENTRAL ANGLE

Sum of Central Angles =

CENTRAL ANGLE

Central Angles separates a circle into __________

Arcs on P: 2 letters: 3 letters:

TYPES OF ARCS

Measurement of an Arc = Measurement of the central Angle

Minor: < 180° Semi-circle: = 180° Major: > 180°

EXAMPLE

Find mRTS and mQTR

EXAMPLE

Find mCZD and mBZC

EXAMPLE

In P, mNPM=46, bisects KPM, and . Find m. Find m Find m

HOMEWORK

Page 533 14 - 31

ANGLE AND ARCS

How can I calculate arc measure? How can I calculate arc length?

EXAMPLE

Find the measure of each central angle.

ARC LENGTH

Another way to measure an arc A fraction of the circumference Proportion:

𝐴360

=𝑙

2𝜋𝑟

Degree measure of central angle

Degrees in a circle

Arc length

Circumference of a circle

EXAMPLE

In B, AC = 9 and mABD = 40. Find the length of .

EXAMPLE

In , AY = 21 and mXAY = 45. Find the length of

HOMEWORK

Page 533 32 - 52

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