circle.notebook
May 12, 2014
I can successfully complete the agenda for the day :)
ShakNOW
Agenda:
• ShakNOW
• Circles­ central angle
• homework
Reminders:
• Review­ Locus Rm 249
• Practice Test 5.23
• Test 5.28
1) How many degrees in full circle?
2) How many degrees in half circle?
3) How many degrees in quarter of a circle?
shakNOW
Circles Packet
Name ________________
Period ____
packet
1
circle.notebook
May 12, 2014
I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
Intro to Circle- Definitions
Intercepted arc ...add
Name
Definition
Diagram
Notation
Name your circle.
1. Circle (p. 566)
2. Radius (p. 566)
3. Central Angle (p. 566)
4. Minor Arc (p. 567)
Is a set of all points equidistant from a given point called the center. A
Draw 2 radii and label points A and B on the circle.
B
Is half a circle Name your arc.
Highlight or bold the minor arc. Label your points.
O
B
A
Highlight or bold the major arc. Label your points.
Name your arc.
O
B
C
6. Semicircle (p. 567)
Name your central angle.
O
A
Is smaller than a semicircle. Is greater than a semicircle. Name your radius. (The segment with a bar over it.)
Draw and label the radius
O
C
5. Major Arc (p. 567)
O
A
Is a segment that has one endpoint at the center and the other endpoints on the circle. Is an angle whose vertex is the center of the circle. Circle O
Mark and label the center O.
A
C
Highlight or bold one semicircle. Label your points.
O
Name your semicircle.
D
B
A
7. Degree measure of an arc
m AOB
It is equal to the measure of the central angle that intercepts the arc.
O
B
Central angles I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
Central Angles - Theorems
Fact ­ Theorem ­ Postulate
Draw a picture to illustrate the fact.
1. All radii of the same circle are congruent.
2. The measure of a semicircle is 180.
3. The measure of a major arc is 360 minus the measure of its related minor arc.
A
320
40
O
B
This is the Arc Addition Postulate
4. If AB and BC are 2 arcs with a common endpoint, (and not other points in common), then
A
B
AB + BC = ABC and mAB + mBC = mABC.
C
A
5. The measure of a central angle is equal to the measure of the intercepted arc.
O
65
B
Central angles
2
circle.notebook
May 12, 2014
I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
Example I ­ Central Angles
F
In circle O, GOE is a straight angle, m GOE = 180, and m FOG = 80.
80O
The degree measure of FG is 80o. (mFG = 80)
Since mGFE = 180,
1. mFE 80O
2. mFEG G
E
O
40o B
C
90o
is a diameter
Example II ­ Minor and Major Arcs & Arc Addition Postulate
1. Minor Arc: AB + BC = AC
mAC = mAB + mBC
A
O
2. Major Arc AB + BCD = ABD
mABD = mAB + mBCD
D
Central angles
I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
Example III ­ Central Angles and Arc Addition Postulate
A
Let OA and OB be opposite rays and m AOC = 75. Find
1. m BOC
2. mAC
= m AOB ­ m AOC
3. mBC
= m AOC
= m BOC
75o
C
O
D
B
4. mAB
5. mBAC
= m AOB
= mBDA + mAC
or
mBAC ­ mBC
Central angles
3
circle.notebook
May 12, 2014
F
Answers: Central Angles ­ Examples Example I ­ Central Angles
80O
In circle O, GOE is a straight angle, m GOE = 180, and m FOG = 80.
80O
G
The degree measure of FG is 80o. (mFG = 80)
E
O
Since mGFE = 180,
1. mFE 2. mFEG = 180 ­ 80
= 100 + 180
= 100
= 280
40o B
C
Example II ­ Minor and Major Arcs & Arc Addition Postulate
1. Minor Arc: AB + BC = AC
90o
2. Major Arc AB + BCD = ABD
mAC = mAB + mBC
= 90 + 40
= 90 + 180
= 130
= 270
A
O
mABD = mAB + mBCD
D
A
Example III ­ Central Angles and Arc Addition Postulate
Let OA and OB be opposite rays and m AOC = 75. Find
1. m BOC
2. mAC
75o
3. mBC
= m AOB ­ m AOC
= m AOC
= m BOC
= 180 ­ 75
= 75
= 105
C
D
B
= 105 4. mAB
5. mBAC
= m AOB
= mBDA + mAC
= 180
= 180 + 75
or
mBAC ­ mBC
360 ­ 105
= 255
= 255
Central angles
I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
C
T
Central Angles - Classwork
128O
P
Find the measure of each arc below, in circle P.
D
B
your turn
1. TC
2. TBD
3. BTC
4. TCB
5. CD
6. CBD
7. TCD
8. DB
9. TDC
10. TB
11. BC
12. BCD
1. TC
128
2. TBD
180
3. BTC
218
4. TCB
270
5. CD
52
6. CBD
308
7. TCD
180
8. DB
90
9. TDC
232
10. TB
90
11. BC
142
12. BCD
270
homework
4
circle.notebook
May 12, 2014
I can successfully complete my homework today :)
Reminders:
• Review­ Locus Rm 249
• Practice Test 5.23
• Test 5.28
Homework
bottom of page 5
homework
I can identify the central angles & their arcs. I will be able to give you the arc measure given the angle measure & vice versa:)
Pull
Central Angles - Homework
1. Find the measure of the central angle that intercepts an arc with a degree measure of 35o. ______
2. Find the measure of the arc intercepted by a central angle with a measure of 120o. ______
In 3 ­ 10, the endpoints of AOC are on circle O, m AOB = 89, and m COD = 42. Find each measure. 3. m DOA
4. m BOD
5. m BOC
Pull
6. m AOC
B
C
7. mAB
8. mDA
42o
89o
O
9. mBCD
D
A
10. mDAB
Homework #'s 3 ­ 10
Central angles
5
Attachments
pg60.pdf