Download Mar 17 - AG - Inscribed and Circumscribed Angles.notebook

Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
Analytic Geometry
March 17, 2016
March 17, 2016
Inscribed and Circumscribed Angles.
EQ: How is the central angle of a circle and an inscribed angle related?
MCC9‐12.G.C.2 Identify and describe relationships among inscribed angles,
radii, and chords. Include the relationship between central, inscribed, and
circumscribed angles; inscribed angles on a diameter are right angles, the
radius of a circle is perpendicular to the tangent where the radius
intersects the circle.
Apr 11­11:51 AM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
Quiz:
March 17, 2016
Circle Vocabulary
Mar 15­8:30 AM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
Warm­up
1) Find x
2)
Find x
A
240
D
85
x
O
F
B
4)
3) Find arcGHK
N
H
M
71O
L
O
58
K
85
C
x
O
G
March 17, 2016
O
23
P
S 71 - vertical angles
R
J
Oct 26­9:44 AM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Homework Answers
1) 120
4) 234
0
0
2) 123
3) 306
0
5) 125
0
0
6) 8
Apr 11­11:54 AM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Inscribed Angles
Properties of Inscribed Angles
B
2xo
- vertex lies on the circle
- sides are chords of the circle.
C
O
xo
A
- corresponding arc is equal to twice
the measure of the inscribed angle.
arc = 2(angle) or
arc angle = 2 Apr 11­11:56 AM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Let's Practice
A
1)
If <BAC = 31o,
O
B
mBC = ? 62
C
H
2)
If <HGJ = 84o,
G
O
mHJ = ? 168
J
Apr 11­12:01 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
3)
March 17, 2016
Q
P
If mPR = 160o
<PQR = ? 80
O
R
4)
L
If mLN = 240o
<LMN = ? 120
O
N
M
Apr 11­12:08 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Circumscribed Angles
Properties of Circumscribed Angles
x
- vertex lies outside of the circle.
y
- sides are tangents of the circle.
- circumscribed angle and
corresponding arc sum to 180o.
x + y = 180o
Nov 1­4:12 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Let's Practice
5)
6)
75o
x
x
48o
180
-75
180 - 48 = 132
105
360 - 132 = 228
7)
220o
360 - 220 = 140
x
140/2 = 70
x=70
Nov 1­4:24 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
ΔABC is inscribed in circle O.
<ABC = 80o and BC = 120o
B
80o
120o
Find the measures of:
<BAC = 360 - 120 = 240
A
O
C
<ACB = 80 x 2 = 160
160 + 120 = 280
AB =
360 - 280 = 80
AC =
80 x 2 = 160
Apr 11­12:13 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
D
ΔDGE is an equilateral triangle
DF bisects <EDG.
E
Find the measure of:
<DEG = 180 / 3 = 60 for each
O
F
G
March 17, 2016
angle.
DG = 60 x 2 = 120
FE = 60 x 2 = 120
120 / 2 (bisector) = 60
<DGF =
Apr 11­12:15 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
Find the missing measures.
56
y
x
z
w = (180 ­ 125) = 55
x = (180 ­ 56) = 124
y = 180 ­ (55+56)= 69
125
w
z = 180 ­ 69 = 111
Nov 1­4:49 PM
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Mar 17 ­ AG ­ Inscribed and Circumscribed Angles.notebook
March 17, 2016
HW: Worksheet
On‐line and textbook help references: pp. 209 ‐ 518
‐ https://learnzillion.com/lessons/3249‐find‐relationships‐between‐central‐and‐circumscribed‐angles
‐ https://www.khanacademy.org/math/geometry/cc‐geometry‐circles/central‐inscribed‐circumscribed/e/central‐‐
inscribed‐‐and‐circumscribed‐angles
‐ http://www.cliffsnotes.com/math/geometry/circles/arcs‐and‐inscribed‐angles
Nov 2­5:37 PM
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