GEOMETRY: Chapter 10
10.2: Arcs and Chords
A central angle of a circle is an angle whose
vertex is the center of the circle. In the
diagram, angle ACB is the central angle of
circle C.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 659.
Use the diagram from last slide:
If m  A C B is less than 180 , then the points on
o
C
that lie in the interior of m  A C B form a m ino r arc
w ith endpoints A and B .
T he points on
C that do not lie on m inor arc A B
form a m ajor arc w ith endp oints A and B . A sem icircle
is an arc w ith endpoints that are the en dpoints of a diam eter.
N am ing A rcs: m inor arcs are nam ed by end points.
M ajor arcs are nam ed by endpoints and on e point
in betw een the endpoints such as A D B .
Measuring Arcs: The measure of a minor arc is
the measure of its central angle.
T h e ex p ressio n m A B is read as "th e m easu re o f arc A B ."
The measure of the entire circle is 360o. The measure
of a major arc is the difference between 360o and
the measure of the related minor arc. The measure of
a semicircle is 180o.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 659.
Ex.1:
Find the m easure of each arc of
C,
w here A B is a diam eter.
a. D B
b. D A B
c. A D B
Answer: a. 135o; b. 225o ; c.180o
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660.
Postulate 23:
Arc Addition Postulate
The measure of an arc formed by two
adjacent arcs is the sum of the measures
of the two arcs.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660.
Ex. 2: A result of a survey about the ages of people
in a town are shown. Find the indicated arc
measures.
a .m R U
b .m R ST
c .m R V T
d .mU ST
Answer: a. 140o ; b. 130o ; c. 230o ; d. 270o
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 660.
Congruent Circles and Arcs
Two circles are congruent circles if they
have the same radius. Two arcs are
congruent arcs if they have the same
measure and they are arcs of the same
circle or of congruent circles.
If C is congruent to D ,
then you can w rite
C 
D.
Ex. 3:
T ell w hether arcs C D and E F are congruent.
E xplain w hy or w hy not.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.661.
Ex. 3:
T ell w hether arcs C D and E F are congruent.
E xplain w hy or w hy not.
Images taken from: Geometry. McDougal Littell: Boston, 2007. P.661.
10.2, p. 607