6.2
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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” C o 50 B A D The measure of the entire circle is ______.The measure of a major arc is the difference between ______ and the measure of the related minor arc. o 360 o 360 The measure of a semicircle is ____. o 180 o 50 AB m o 310 ADB m
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6.2. Find Arc Measures. The measure of a minor arc is the measure of its central angle. The expression m AB is read “the measure of arc AB”. A. B. C. D. Measuring Arcs. - PowerPoint PPT Presentation
Transcript of 6.2
6.2 Find Arc Measures
Measuring ArcsThe measure of a minor arc is the measure of its
central angle. The expression mAB is read “the measure of arc AB”
Co50 B
A
D
The measure of the entire circle is ______.The measure of a major arc is the difference between ______ and the measure of the related minor arc.
o360o360
The measure of a semicircle is ____.o180
o50AB mo310ADB m
6.2 Find Arc Measures
Example 1 Find measures of arcsFind measures of arcs
Find the measure of each arc of C, where DF is the diameter.
F
C
ED
o117
DE a. DFE b. DEF c.
.________DE so arc, ______ a is DE a. mm
arc, ______ a is DFE b.
.____________DFE m
.____DEF m
minor DCE o117
majoro360 o117 o243
semicircleo180
and _________, a is DEF so diameter, a is DF c.
6.2 Find Arc MeasuresCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 1. Find mRTS in the diagram at the
right. o45R
T
SP
arcmajor a is RTS
RScircle entire RTS mm oo 45360
o315
6.2 Find Arc Measures
Arc Addition PostulateThe measure of an arc formed
by two adjacent arcs is the sum of the measures of the two arcs.
________ABC mmm
BA
C
AB BC
=_____ + _____
6.2 Find Arc Measures
Example 2 Find measures of arcsFind measures of arcsMoney 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.
BD a. m BCD b. m
o55
D
BChecking
A
C
MoneyMarket
Bonds
Savings
o55
o140
o60
o105
Solution
ADBA BD a. mmm o105
=_____o160
BD603 BCD b. o mm
= 360o _____o160
=_____o200
6.2 Find Arc Measures
Congruent CirclesTwo circles that have the same radius.
Congruent ArcsTwo arcs that have the same measure and
are arcs of the same circle or congruent circles.
the same circle
6.2 Find Arc Measures
Example 3 Identify congruent arcsIdentify congruent arcsTell whether the given arcs are congruent. Explain why or why not.
Solution
_____in________ are they because DE __ BC a.
DE and BC a. o75o75
C
B E
D
DE.BC___ and mm
arebut they ________, same thehave CD and AB b. measure
6.2 Find Arc Measures
Example 3 Identify congruent arcsIdentify congruent arcsTell whether the given arcs are congruent. Explain why or why not.
Solution
CD and AB b.
thatcircles of arcs are they because __________
o80C
A
B
D
not congruent
_.__________ are not congruent
______________in are they because HJ __FG b. congruent circles
6.2 Find Arc Measures
Example 3 Identify congruent arcsIdentify congruent arcsTell whether the given arcs are congruent. Explain why or why not.
Solution
HJ andFG c. F
G
H
J
HJ.FG___ and mm
6.2 Find Arc MeasuresCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises. 2. In Example 2, find (a) mBCA and
(b) mABC
arcmajor a isBCA
ABcircle entireBCA mm oo 55360
o305D
BChecking
A
C
MoneyMarket
Bonds
Savings
o55
o140
o60
o105
a.
arcmajor a is ABCb.
BCAB ABC mmm oo 14055
o195
6.2 Find Arc MeasuresCheckpoint. Complete the following exercises. Checkpoint. Complete the following exercises.
Q
S
R
P
2. In the diagram at the right, is PQ SR? Explain why or why not.
SRPQ Because they are in the same circle and
SRPQ mm
6.2 Find Arc Measures
Pg. 204, 6.2 #1-38
