warm-up
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Warm-up. Find the measure of each arc. Homework Review. CCGPS Geometry 10.21.14. UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: How do we use angle measures to find measures of arcs? - PowerPoint PPT PresentationTRANSCRIPT
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Warm-upFind the measure of each arc.
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Homework Review
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CCGPS Geometry10.21.14
UNIT QUESTION: What special properties are found with the parts of a circle?Standard: MMC9-12.G.C.1-5,G.GMD.1-3
Today’s Question:How do we use angle measures to find measures of arcs?Standard: MMC9-12.G.C.2
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Inscribed Angles
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Inscribed Angle: An angle whose
vertex is on the circle and
whose sides are chords of the circle
INSCRIBEDANGLE
INTER
CEP
TED
ARC
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
C
L
O
T1.
YES; CL
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Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle.
Q
R
K
V2. NO;
QVR
S
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2
ArcdIntercepteAngleInscribed
160
80
To find the measure of an inscribed angle…
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120
x
What do we call this type of angle?What is the value of x?
y
What do we call this type of angle?How do we solve for y?The measure of the inscribed angle is HALF the
measure of the inscribed arc!!
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Examples
3. If m JK = 80, find m JMK.
M
Q
K
S
J
4. If m MKS = 56, find m MS.
40
112
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72
If two inscribed angles intercept the same arc, then they are congruent.
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Example 5
In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.
3
Q
D
JT
U
4
x = 3
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If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.
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2 Column Proof
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A circle can be circumscribed around a quadrilateral if and only if its
opposite angles are supplementary.
A B
CD
180 CmAm180 DmBm
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z
y
110
85
110 + y =180y = 70
z + 85 = 180z = 95
Example 8 Find y and z.
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180
diameter
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
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H
K
GN
4x – 14 = 90
Example 6
In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
x = 26
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H
K
GN
6x – 5 + 3x – 4 = 90
Example 7
In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x.
x = 11
1
2
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Homework:
• Worksheet