Use Inscribed Angles and Polygons

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Use Inscribed Angles and Polygons

• 10.4

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Vocabulary

• Inscribed Angle an angle that has a vertex on
  the circle. The sides of the angles are chords.
• Intercepted Arc the arc that is contained in the
  inscribed arc.

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Whats the difference?
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Important
The measure of the arc is half the size of the
inscribed angle.
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Find the measure
If we want to find the measure of arc QT, what do
we do with the measure of the inscribed angle
óTRQ?
100º
Multiply both sides by 2
Simplify
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Find the indicated measurement
46º
92º
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Find the indicated measurement
The arc is twice the inscribed angle
84º
172º
86º
A circle is 360º
360 84 172 104º
104º
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Find the indicated value
A semi-circle is 180º
180 125 55
10º
The inscribed angle is half the arc.
55º
27.5º
O
115º
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Lets think
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Name the angles that are congruent to each other.
With this theorem we basically know that there
are 2 proportional triangles.
Recall that proportional triangles have congruent
angles.
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Find a and b
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In inscribed quadrilaterals the opposite angles
are supplementary.
95 q 180
q 85
P 110 180
p 70
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Find a and b
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