goemetry/notes 10.2
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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
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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
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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