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5.1 Arcs Intro
Contribuição de: Smith
(Autor original: Lehnert)
Just as a SECTOR
of a circle is part of
the AREA.......

An ARC of a circle
is part of the
CIRCUMFERENCE
The ARC of a circle has the same angle measure
as the central angle that forms it.
120
arc
?
central angle
?

MQ and NR are diameters.  Find the indicated

measure.

(arc MN has the same measure as angle MON)
N

M

82
P
O
63
Q

arc MN =

R

MQ and NR are diameters.  Find the indicated

measure.

(arc MN has the same measure as angle MON)
N

M

82
P
O
63
Q

arc MN =

R
Vertical
Angles
are ≅
63

MQ and NR are diameters.  Find the indicated

measure.

arc QR
N

M

82
P
O
63
Q
R

MQ and NR are diameters.  Find the indicated

measure.

N

M

82
P
O
63
Q

arc PQ =

R
Every
diameter
has a
central angle
of 180.

MQ and NR are diameters.  Find the indicated

measure.

N

M

82
P
O
63
Q

arc PQ =

R
Central angle
   180
   -82
   -63

    35
35

MQ and NR are diameters.  Find the indicated

measure.

arc NQ
N

M

82
P
O
63
Q
R

MQ and NR are diameters.  Find the indicated

measure.

arc NQR
N

M

82
P
O
63
Q
R

MQ and NR are diameters.  Find the indicated

measure.

arc MR
N

M

82
P
O
63
Q
R

MQ and NR are diameters.  Find the indicated

measure.

arc PRN
N

M

82
P
O
63
Q
R
120
70
120
120
70
Congruent chords
form congruent arcs
Congruent chords
form congruent arcs

Find arc MN.

M

P
N
68
Q

Find arc MN.

M

P
N
76
Q

M

4x
P
N
80
Q
Congruent chords
form congruent arcs
4x =
x =
The arc MN
is congruent to
to which arc?????

M

85
P
N
 arc MP
 arc PQ
 arc QN
 arc MQ
65
Q

M

85
P
N
65
Q
Arc MN is congruent to arc PQ.
(≅ chords form ≅ arcs)


If arc MN is represented by
the variable x,
what variable should be
used to represent
congruent (≅) arc PQ?
Complete the
equation with
the total
measure
of every arc
on the circle
85+65+x+x =

M

x
85
P
N
65
x
Q

M

x
85
P
N
65
x
Q
85+65+x+x =
+
= 360
360

M

x
85
P
N
65
x
Q
-150
150
85+65+x+x =
+
2x
2x =
x =
= 360
360
-150
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