Download 10.4 inscribed angles.notebook

10.4 inscribed angles.notebook
March 07, 2016
3/7/16 ­ Warm Up Problem
Find the measure of each arc.
E
D
24o
C
A
B
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10.4 inscribed angles.notebook
March 07, 2016
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10.4 inscribed angles.notebook
March 07, 2016
Section 10.4 ­ Inscribed Angles
Inscribed Angle — an angle whose vertex is on a circle and whose sides are chords.
Intercepted Arc — the arc on the interior of an inscribed angle.
B
<ABC is an inscribed angle
A
ADC is an intercepted arc
D
C
R
S
K
T
J
L
Inscribed Angle: Inscribed Angle: Intercepted Arc:
Intercepted Arc:
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10.4 inscribed angles.notebook
March 07, 2016
Measure of Inscribed Angles
110
o
Do the central angle and the inscribed angle appear to be the same measure?
Theorem 10.7 ­ Measure of an Inscribed Angle Thm
The measure of an inscribed angle is half the measure of its intercepted arc.
2 x inscribed angle = arc measure
A
B
30
o
60o
C
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10.4 inscribed angles.notebook
March 07, 2016
Find the value of x.
G
K
86o
J
R
54o
F
x
L
x
S
x
42o
T
H
x
S
N
R
M
x
52
o
L
Q
5
10.4 inscribed angles.notebook
March 07, 2016
Intercepting the Same Arc
64
o
What is the measure of x?
xo
What is the measure of y?
yo
Theorem 10.8 If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
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10.4 inscribed angles.notebook
March 07, 2016
Inscribed Polygons
­ a polygon is inscribed in a circle if each of its vertices lie on the circle
Theorem 10.9
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.
If a triangle is inscribed in a semicircle, then it is a right triangle.
H
Theorem 10.10
y
o
J
G
x
o
125
o
75
o
A quadrilateral can be inscribed in a circle if and only if its opposite angels are supplementary.
K
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10.4 inscribed angles.notebook
March 07, 2016
Find the value of the variable or the measure of the numbered angle.
40o
2ao
4bo
6
80o
5
1
2
2bo
100o
2ao
3
4
140o
8
10.4 inscribed angles.notebook
March 07, 2016
Assignment:
pg. 676
(3­18)
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