Download 9-3 Arcs and Central Angles

Honors Geometry_9.3_March 2
Warmup
1) Solve for x.
C is center
P is point of tangency
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C
x
8
2) Solve for x and y.
P
Both the Blue line and purple line
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Revisit THEOREM 9.1 if necessary
are tangent to the circle
x
18
y
18
60˚
9-3
Arcs and Central Angles
I can ... explain how to find the measure of a given arc or a given
central angle.
I can... solve real world problems involving central angles and
arcs of circles. [G.CO.1, G.C.2]
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Honors Geometry_9.3_March 2
CENTRAL ANGLE - an angle with its vertex at the center of the
circle & whose two sides are radii.
ARC - portion of the edge of the circle defined by two endpoints.
MINOR ARC
- arc that is in the interior of the central ∠.
- measure will be less than 180˚.
- Use 2 letters to name.
MAJOR ARC
- arc with a measure greater than 180˚
- Use 3 letters to name.
SEMICIRCLE
- arc with endpoints on the diameter.
- measure equals 180˚.
- Use 3 letters to name.
MEASURING ARCS
Measures of arcs are related to corresponding central angles.
measure of a minor arc - the measure of its central angle
measure of a major arc - 360˚ minus the measure of the minor arc.
measure of a semicircle - 180˚
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Honors Geometry_9.3_March 2
Two arcs of the same circle are adjacent if they intersect at
exactly 1 point. You can add the measures of adjacent angles using...
Arc Addition Postulate:
The measure of the arc formed by 2 adjacent arcs is the sum of
the measures of the 2 arcs.
Two arcs of the same circle or of congruent circles are congruent
arcs if they have the same measure.
Theorem 9.3
In the same circle or in congruent circles, 2 minor arcs are
congruent if and only if their central angles are congruent.
50o
50o
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Honors Geometry_9.3_March 2
Name the following: (O is the center)
a) two minor arcs
b) two major arcs
c) two semicircles
C
,
, etc.
R
O
d) an acute central angle
S
A
e) two congruent arcs
Give the measure of each angle or arc. YT is a diameter.
a) mWX = _______
b) mXY = _______
Y
X
30 o
c) m∠WOT = _______
d) mYZT = _______
e) m∠YOT = _______
O
Z
W
50
o
T
f) mXYT = _______
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Honors Geometry_9.3_March 2
Find:
D
E
4
-1
x
2
4x
2x
3
3x x+1
0
A) mAB = _____
C
B) mEDB = ______
B
A
[first find 'x']
Assignment P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16
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Honors Geometry_9.3_March 2
9.3 Assignment: P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16
150˚
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Honors Geometry_9.3_March 2
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Honors Geometry_9.3_March 2
Answers
2)80
4) 50
6) 55
7) 30
8) 4,8
10)
60
30
11)
16) 35
70, 70
2n
3k
56 50 2x
70
50 2x
35 28
#10 & 11 HINT:
Make isosceles triangles
34 44
100 88
104 p + q
50 44 50
1/2(p+q)
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