1 sect. 10.3 inscribed angles goal 1 using inscribed angles goal 2 using properties of inscribed...
TRANSCRIPT
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Sect. 10.3 Inscribed Angles
Goal 1 Using Inscribed Angles
Goal 2 Using Properties of Inscribed Angles.
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Using Inscribed Angles
An INSCRIBED ANGLE is an angle whose vertex is on the circle and whose sides each contain chords of a circle.
Inscribed Angles & Intercepted Arcs
D
B A
C
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Using Inscribed Angles
INSCRIBED angle Central angle Vertex on circle Vertex on center
Difference between inscribed angles andCentral angles:
D
B A
C
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Using Inscribed Angles
If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc.
m = m arc OR 2 m = m arc
Theorem 10.8 – Measure of an Inscribed Angle
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1
50°
100°
B
AC
50°
100°
B
AC
50°
100°
B
AC
x°
2x°
B
AC
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Using Inscribed Angles
Example 1:
63
Find the mPAQ
and .PQ
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Using Inscribed Angles
Find the measure of each arc or angle.
QSR
Example 2:
Q
R
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Using Inscribed Angles
Theorem 10.9If two inscribed angles intercept the same arc or arcs of equal measure then the inscribed angles have equal measure.
mACD = mABD
P
A
BC
D
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Using Inscribed Angles
Example 3:
70E D
A
FEDFmFind
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Using Properties of Inscribed Angles
Example 4:
41°
60°
P
C
DA
B
Find mCAB and m AD
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Using Properties of Inscribed Angles
Inscribed PolygonA polygon whose vertices lie on the circle.
Quadrilateral ABFE is inscribed in Circle O.
O
A
B
F
E
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Using Properties of Inscribed Angles
A polygon is circumscribed about a circle if and only if each side of the polygon is tangent to the circle.
Circumscribed Polygon
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Using Inscribed Angles
E DA
B
F
Example 5:
Find mEFD
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Using Properties of Inscribed Angles
A triangle inscribed in a circle is a right triangle if and only if one of its
sides is a diameter.
Theorem 10.10
A has its vertex on the circle, and it intercepts half of the circle so thatmA = 90.
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Using Properties of Inscribed Angles
If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.
Theorem 10.11
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Using Properties of Inscribed Angles
Find the measure ofGDE
Example 6:
Find x. 3x°E
D
A
B
C
F
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Using Properties of Inscribed Angles
Find x and y
3x°
(y + 5)°
(2y - 3)°
85°80°
y°x°
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Homework:work sheet will be
provided in class