Inscribed Angles Lesson 10.3bCalifornia 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
definitionsInscribed Polygon
A polygon with all of its vertices on a circle.Circumscribe
To circle around something.
A
B C
D
EF
P
hexagon is inscribed in
ABCDEFP
circumscribeshexagon
PABCDEF
example Find value of x and y.
8xo8xo
3yo
6yo
theoremInscribed Right Triangle
An inscribed right triangle has a diameter as its hypotenuse.
C
Q
P
R
is a right trianglePQR is a diameterPR
example
B
DA
C
Find the measure of the arc or angle.
180omADC
example
C
B
A
3xo
3 90x
30x
Find value of x.
theoremInscribed Quadrilateral
A quadrilateral can be inscribed in a circle if and only if its opposite angles are
supplementary.
S
Q
P
R
180
180
m P m R
m Q m S
85 180y 95y
100x 80 180x
example
TS
R85o
U80o
xo yo
Find value of x and y.
220 190 1800760 190 3420
x yx y
22 19 180x y
example
B
A
D
22xo
C40xo10yo
19yo
Find value of the measure of each angle.
3x 540 1620x
40 10 180x y -10( )19 ( )
22(3) 66m D
40(3) 120m C
example
B
A
D
22xo
C40xo10yo
19yo
Find value of the measure of each angle.
180 114m B m D
180 60m A m C
120o
66o
60o
114o
11
Today’s Assignment
Tribe Pride
always my best effort.
p.617: 16, 18 – 29
Find the value of each variable. Explain.
Can the quadrilateral always be inscribed in a circle? Explain your reasoning.
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