Arcs

1
Arcs Chords of CirclesSection 10.2

• Goal
• To use properties of arcs and chords of circles.

2
Central Angle

• The sum of the measures of the central angles of
  a circle is 360.

A
B
P
E
3
Measures of Arcs

P
M
C
E
4
Measures of Arcs

M
C
E
D
5
Example
B
C
A
148
D
6
Arc Addition Postulate

B
C
A
D
7
Congruent Arcs

Congruent arcs are arcs that have the same
measure and are of the same or congruent circles.
A
B
57
57
D
C
Z
X
65
Y
W
8
Congruent Arcs
X
Y
C
Z
9
Theorem 10.4
In the same circle or in congruent circles, two
minor arcs are congruent if and only if their
corresponding chords are congruent.
A
Q
C
B
10
Theorem 10.5
If a diameter of a circle is perpendicular to a
chord, then the diameter bisects the chord and
its arc.
H
D
E
G
F
11
Theorem 10.6
If one chord is a perpendicular bisector of
another chord, then the first chord is a diameter.
H
E
G
D
F
12
Theorem 10.7
In the same circle or congruent circles, two
chords are congruent if and only if they are
equidistant from the center.
H
D
C
B
A
F
G
13
Example
A
F
C
B
5
E
D
14
Example
B
C
60
A
82
100
D
E