Download 10.2 + 10.3 - Arcs + Chords.notebook

10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
3/3/16 - Warm Up Problem
Write a good definition of a circle.
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Section 10.2 - Find Arc Measure
Goals:
identify special segments in circles, central angles, and arcs
find the measure of central angles and arcs
Circle: set of all points in a plane that are equidistant from a given point (center).
Radius: segment from the center to a point on the circle.
Diameter: segment across a circle through the center
center
2 * radius = diameter
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Naming Parts of a Circle
Name the circle.
Name a radius of the circle.
Name a diameter of the circle.
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Measures of Central Angles
Central Angle: an angle whose vertex is the center of the circle.
­its sides are two radii
All of the central angles of
a circle must add up to
360 degrees
Find the measure of each central angle.
84o
35o
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Finding Arc Measures
Arc: part of the outside edge of a circle.
A
• Arcs are measured in degrees
• The measure of an arc is equal to the measure of its corresponding central angle
86o
D
B
C
Minor Arc: an arc that is smaller than 180o
Semicircle: an arc that is exactly 180o Major Arc: an arc that is greater than 180o
Naming an Arc
- use the letters of the points at either end and one
more point in the middle if there is one
- put the arc symbol on top
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Measure of an arc = Measure of its central angle
C
Find the measure of each arc.
A
55o
F
B
D
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
A
B
What type of special segment
are AB and CD?
Do AB and CD appear to be
congruent?
C
D
What else in the circle is
congruent when AB and CD are
congruent?
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Section 10.3 - Apply Properties of Chords
Goal: use relationships between chords, arcs, and other
segments in circles to find measures
Chord: a segment whose endpoints are on the circle
Theorem 10.3
In the same circle, or in congruent
circles, two minor arcs are congruent
if and only if their corresponding
chords are congruent.
B
D
A
C
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
B
Theorem 10.4
If one chord is a perpendicular
bisector of another chord, then
the first chord is a diameter.
Theorem 10.5
If a diameter of a circle is
perpendicular to a chord, then the
diameter bisects the chord and
its arc.
C
T
V
A
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Theorem 10.6
In the same circle, or in
congruent circles, two chords
are congruent if and only if
they are equidistant from
the center.
D
R
Z
H
G
E
V
Find the value of x for each circle.
x
3
5
3
5
yo
x
48o
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Find each measure.
F
RT
AB
A
R
8
D
6
CS
36o
B
C
T
U
S
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10.2 + 10.3 ­ Arcs + Chords.notebook
March 03, 2016
Assignment:
pg. 661 (3-10)
pg. 667 (3-15)
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