Download - Arcs and Chords lesson 10.2a
Arcs and Chords lesson 10.2aCalifornia State
Standards4: Prove theorems involving
congruence and similarity7: Prove/use theorems
involving circles.21: Prove/solve relationships
with circles.
Lesson GoalsFind the measure of arcs in a circle using the definition of arc measure and the arc addition postulate.
ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers
definitionsCentral Angle
An angle whose vertex is the center of a circle.
Minor ArcA section of the circle cut by a central angle
that measures less than 180o
The measure of an minor arc equals the measure of its central angle.
definitions
C
A
B
mAB m ACB
definitionsMajor Arc
A section of the circle that measures more than 180o.The measure of a major arc equals the difference
between 360o and the measure of its associated minor arc.
SemicircleAn arc with endpoints coinciding with the endpoints
of a diameter
definitions
C
A
B
D 360mADB mAB
definitions
C
P
Q
180mPQ
180omEHI
328omHIE
example
C
HI
E
Find the measure of each arc.
148o
32omEH
mSE 118o
mSET 218o
mST
example
C
D
T
S
Find the measure of each arc.
82o
142o
60o
100o
E
m ACB m ECD
AB DE
definitionsCongruent Arcs
Arcs with the same measure within the same circle or congruent circles.
C
A
BD
E
because
mCE 70o
AB CE
mAB
You try Find the measure of each arc.
70o
D
A
E
110o
C
B
mBD
mAE
Yes Is ? AE BD
example
C
B
D
A
E
210o
Find the measure of each arc.
150o
150o
example Find the measure of each arc.
36o
36o
144o
13
Today’s Assignment
Tribe Pride
always my best effort.
p. 607: 12 – 38
Determine whether the arc is a minor arc,a major arc, or a semicircle of circle R.
and are diameters. COPYthe diagram. Find the indicated measure.KN JL
Find the measure of the red arc. Use circle P to find the value of x. Then find the measure of the red arc.
35. Name 2 pairs of congruent arcs in #32 – 34. Explain your reasoning.