Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its...
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Transcript of Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its...
![Page 1: Inscribed Angles By the end of today, you will know what an inscribed angle is and how to find its measure.](https://reader036.fdocuments.net/reader036/viewer/2022090107/5a4d1bde7f8b9ab0599de234/html5/thumbnails/1.jpg)
Inscribed AnglesBy the end of today, you will know what an
inscribed angle is and how to find its measure.
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An inscribed angle is an angle whose vertex is on a circle.
Inscribed Angle
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The arc that lies in the interior of an inscribed angle and has endpoints on the angle.
Intercepted Arc
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The measure of an inscribed angle is half the measure of its intercepted arc.
Measure of an Inscribed Angle Theorem 10.10
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Theorem 10.11
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
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Inscribed Polygon
A polygon is an inscribed polygon if all of its vertices lie on a circle.
The circle that contains the vertices is circumscribed circle.
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If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle.
Theorem 10.12
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A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
Theorem 10.13
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p.562: 3-15
Practice Problems