Inscribed Angles Lesson 10.3a
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Transcript of Inscribed Angles Lesson 10.3a
Inscribed Angles Lesson 10.3aCalifornia State
Standards
4: Prove theorems involving congruence and similarity7: Prove/use theorems involving circles.21: Prove/solve relationships with circles.
Lesson Goals
Find the measures of arcs and angles within a circle by using the Inscribed Angle Measure Theorem and the Congruent Inscribed Angles Theorem.
ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers
definitionInscribed Angle
An angle whose vertex is on a circle and whose sides contain chords of the circle.
P
QR
definitionIntercepted Arc
An arc that lies in the interior of an inscribed angle
and has endpoints on the angle.P
QR
12 mAB
theoremInscribed Angle Measure
The measure of an inscribed angle is half the measure of its intercepted arc.
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A
B
m ACB
D
example
B
C
140o70o
Find the measure of the arc or angle.
A
mAC
C
theoremCongruent Inscribed Angles
Inscribed anglesare congruent.
B
A
E AAEB CB
that intercept the same arc
m ADE
m ACE
m ABE
example
CB
D
A
E90o
45o
45o
45o
Find the measure of the arc or angle.
example
B
A
C98o
196o
Find the measure of the arc or angle.
m ABC
D
m C
example
CB
D
44o44o
Find the measure of the arc or angle.
A
m PON
60o
35o
130o
90o
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Today’s Assignment
Tribe Pride
always my best effort.
p. 616: 6, 7, 9 – 15, 17, 35, 43
Find the measure of the blue arc or angle.
Find the value of each variable. Explain.