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Geometry 10.4 3­26.notebook
March 27, 2015
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10.4 Inscribed Angles and Polygons
Bell Work
1. The measure of the interior angles of a quadrilateral are 80 degrees, 100 degrees, 55 degrees, and 5x degrees. Find the value of x.
2. Solve 3x = (4x + 12)
Jan 19­9:30 PM
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Geometry 10.4 3­26.notebook
March 27, 2015
10.4 Inscribed Angles and Polygons
Theorem 10.7 Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is one half the measure of its intercepted arc.
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Theorem 10.7: three cases
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Geometry 10.4 3­26.notebook
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Example 1
Find the indicated measure in circle P.
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Theorem 10.8 If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
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Geometry 10.4 3­26.notebook
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Example 2
Find mRS and m STR. What do you notice about angle STR and angle RUS?
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Geometry 10.4 3­26.notebook
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Example 3
Find the measure of the red arc or angle.
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Theorem 10.9
If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. Jan 19­9:54 PM
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Geometry 10.4 3­26.notebook
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Theorem 10.10
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. Jan 19­10:04 PM
Example 4
Find the value of each variable. Jan 19­10:13 PM
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Geometry 10.4 3­26.notebook
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Assignment
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10.4 WB with 10.5
#1-15, 17, 18, 22
197
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Geometry 10.4 3­26.notebook
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Geometry 10.4 3­26.notebook
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