arcs and chords lesson 10.2b california state standards 4: prove theorems involving congruence and...
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Arcs and Chords lesson 10.2bCalifornia State
Standards
4: Prove theorems involving congruence and similarity
7: Prove/use theorems involving circles.
21: Prove/solve relationships with circles.
Lesson Goals
Find 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
iffAB PQ
theoremCongruent Arcs and Chords
Two minor arcs are congruent if and only iftheir corresponding chords are congruent.
C B
Q
P
A
AB PQ
if AB PQ
theoremCongruent Arcs and Chords
Two minor arcs are congruent if and only iftheir corresponding chords are congruent.
C B
Q
P
A
then AB PQ
theoremDiameter-Chord
A diameter that is perpendicular to a chord bisects the chord and its arc.
C
E
AE BE and AD BD
A
D
B
is a diameterDF
is the bisector of DF AB
theoremDiameter-Chord Converse
If one chord is the perpendicular bisector of another chord,
then the first chord is a diameter.
C
B
A
D
E
F
then CR CD
If , then .
CR CDPQ AB
theoremsCongruent Chords
Two chords are congruent if and only if they are equidistant from the center.
C B
Q
P
A
R
D
If PQ AB
mBD
3 11 2 48x x 11 48x
37x
Find mBD
example
C
B
DE
(2x + 48)o(3x + 11)o
2(37) 48122
mBE 180 10476
mDE 26 78104
4 78x x 3 78x
26x
examples
C
B
D
E
4xo(x + 78)o
Find mBE
P
6FE example
B
C
E
A
D
G
F
AB = 12 DE = 12 CE = 7
Find CG 6
7
2 2 27 6 CF 249 36 CF
213 CF13 CF
CF CG13 CG13
13
Today’s Assignment
Tribe Pride
always my best effort.
608: 39 – 51, 57
What can you conclude about the diagram?State a postulate or theorem that justifies youranswer.
Find the measure of the red arc or chordin circle A. Explain your reasoning.
Find the value of x in circle C. Explain your reasoning.
Do # 48, 57 at home
The time zone wheel shown consists of two concentric circular pieces of cardboard fastened at the center so the smaller wheel can rotate. To find the time in Tashkent when it is 4 P.M. in San Francisco, you rotate the small wheel until 4 P.M. and San Francisco line up as shown. Then look at Tashkent to see that it is 6 A.M. there. The arcs between cities are congruent.
49. What is the arc measure for each time zone on the wheel?50. What is the measure of the minor arc from the Tokyo zone to the Anchorage zone?51. If two cities differ by 180° on the wheel, then it is 3:00 P.M. in one city if and only if it is ? in the other city.