6.2
Find Arc Measures
Measuring Arcs
The measure of a minor arc is the measure of its
central angle. The expression mAB is read
“the measure of arc AB”
A
o
50
B
C
The measure of the entire circle is
o
______.The
measure of a major arc is
360
D
o
the difference between ______
360 and
o
the measure of the related minor arc. mAB  50
o
180 mADB  310o
The measure of a semicircle is ____.
6.2
Find Arc Measures
Example 1 Find measures of arcs
Find the measure of each arc of C,
where DF is the diameter.
D
E
117o
C
F
a. DE
b. DFE
c. DEF
minor arc, so mDE  m DCE
a. DE is a ______
____  117
____ .
o
major arc,
b. DFE is a ______
243 .
mDFE  ____
117  ____
360  ____
o
o
o
semicircle and
c. DF is a diameter, so DEF is a _________,
o
180 .
mDEF  ____
6.2
Find Arc Measures
Checkpoint. Complete the following exercises.
1. Find mRTS in the diagram at the
right.
RTS is a major arc
mRTS  entire circle  mRS
 360  45
o
 315
o
o
R
T
P
45o
S
6.2
Find Arc Measures
Arc Addition Postulate
The measure of an arc formed
by two adjacent arcs is the
sum of the measures of the
two arcs.
BC
AB  m ____
mABC  m ____
A
B
C
6.2
Find Arc Measures
Example 2 Find measures of arcs
Money You join a new bank and divide
your money several ways, as shown in
the circle graph at the right. Find the
indicated arc measures.
B
Checking
o
55
A
Savings
140o
105o
Bonds
b. mBCD
a. mBD
Money
Market
60 o
C
D
Solution
a. mBD  mBA  mAD b. mBCD  360  mBD
o
o
o
105
55 + _____
=_____
o
160
=_____
o
= 360  160
_____
o
=_____
200
o
6.2
Find Arc Measures
Congruent Circles
Two circles that have the same radius.
Congruent Arcs
Two arcs that have the same measure and
are arcs of the same circle or congruent
circles.
6.2
Find Arc Measures
Example 3 Identify congruent arcs
Tell whether the given arcs are congruent. Explain why
D
C
or why not.
a. BC and DE
Solution
o
o
75
75
B
E
the same circle
a. BC __
_____
 DE because they are in________
and mBC___
 mDE.
6.2
Find Arc Measures
Example 3 Identify congruent arcs
Tell whether the given arcs are congruent. Explain why
or why not.
b. AB and CD
A
80
o
C
B
Solution
D
measure but they are
b. AB and CD have the same ________,
not congruent because they are arcs of circles that
__________
not congruent_.
are __________
6.2
Find Arc Measures
Example 3 Identify congruent arcs
Tell whether the given arcs are congruent. Explain why
G
or why not.
c. FG and HJ
H
F
J
Solution
congruent circles
b. FG __
____
 HJ because they are in __________
and mFG___
 mHJ.
6.2
Find Arc Measures
Checkpoint. Complete the following exercises.
2. In Example 2, find (a) mBCA and
(b) mABC
a.
BCA is a major arc
 360  55
 305
a major arc
mABC  mAB  mBC
 55  140
 195
o
Money
Market
140o
105o
Bonds
o
60
D
b. ABC is
o
A
o
o
o
55
Savings
mBCA  entire circle  mAB
o
B
Checking
o
C
6.2
Find Arc Measures
Checkpoint. Complete the following exercises.
2. In the diagram at the right, is
PQ SR? Explain why or why not.
PQ  SR
P
Q
Because they are in the same circle and
mPQ  mSR
S
R
6.2
Find Arc Measures
Pg. 204, 6.2 #1-38