warm up april 22
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Warm up April 22. EOCT Week 14 #2. Review HW. Case I: Central Angle: Vertex is AT the center. A. . P. B. Case II: Inscribed Angle: Vertex is ON circle. . ANGLE. ARC. ARC. . ANGLE. 160 . The arc is twice as big as the angle!!. 80 . Find the value of x and y. 120 . . - PowerPoint PPT PresentationTRANSCRIPT
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Warm up April 22
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EOCT Week 14 #2
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Review HW
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P
A
B
Central ANGLE = ARC
Case I: Central Angle: Vertex is AT the center
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Case II: Inscribed Angle: Vertex is ON circle
ANGLE = ARC
2ANGLE
ARCANGLE
ARC
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2 ArcdIntercepteAngleInscribed
160
80
The arc is twice as big as the angle!!
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120
x
y
Find the value of x and y
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Examples1. If mJK = 80 and JMK = 2x – 4, find x.
M
Q
K
S
J
2. If mMKS = 56, find m MS.x = 22
112
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72˚
If two inscribed angles intercept the same arc, then they are congruent.
Find the measure of DOG and DIG D
O
G
I
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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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a quadrilateral inscribed in a circle: opposite angles are
supplementary.A B
CD
180 CmAm180 DmBm
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If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
diameter
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Example 3In J, m3 = 5x and m 4 = 2x + 9.Find the value of x.
3
QD
JT
U
4x = 3
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4x – 14 = 90
HK
GN
Example 4In K, GH is a diameter and mGNH = 4x – 14. Find the value of x.
x = 26
Bonus: What type of triangle is this? Why?
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z
y
110
85
110 + y =180y = 70
z + 85 = 180z = 95
Example 5 Find y and z.
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Inscribed Quadrilaterals
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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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Vocab• inscribed quadrilateral a
quadrilateral whose vertices are on a circle
• inscribed triangle a triangle whose vertices are tangent to a circle
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If a right triangle is inscribed in a circle then the
hypotenuse is the diameter of the circle.diameter
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4x – 14 = 90
HK
GN
In K, GH is a diameter and m<GNH = 4x – 14. Find the value of x.
x = 26
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a quadrilateral inscribed in a circle: opposite angles are
supplementary.A B
CD180 CmAm
180 DmBm
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z
y
110
85
110 + y =180y = 70
z + 85 = 180z = 95
Find y and z
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Practice WSGet in your
groups please.
12 problems
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Homework WSDay 21
Inscribed Angles
Choose even or odd problems