Geometry/Notes 10.4
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Transcript of Geometry/Notes 10.4
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SECTION 10.4Inscribed Angles
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INSCRIBED ANGLES
How do I find the measure of an inscribed angle?
How do I find the measures of the angles of an inscribed polygons?
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INSCRIBED ANGLE
Inscribed Angle: Angle with the vertex on the circle and the sides are chords.
Intercepted Arc: The arc created by the chords.
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INSCRIBED ANGLE
Inscribed and central angles are different!
Inscribed =
Central =
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INTERCEPTED ARCS
Which are the intercepted Arcs?
Inscribed =
Central =
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THEOREM 10.4
Inscribed Angle Theorem – If an angle is inscribed in a circle, then the measure of the angle is ½ the measure of the intercepted arc.
A
B
C
D
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THEOREM 10.4
If what is ?
If 48,what is ?
If = 230,what is ?
A
B
C
D
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EXAMPLE
In F, = 20, = 40, = 108, and . Find the measures of the numbered angles.
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THEOREM
Theorem 10.6: If two inscribed angles of a circle intercept congruent arcs or the same arc, then the angles are congruent.
A B
CD
A B
CD
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THEOREM
Theorem 10.7: If an inscribed angle intercepts a semicircle, the angle is a right angle.
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EXAMPLE
Triangles TVU and TSU are inscribed in with . Find the measure of each numbered angle if and .
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THEOREM
Theorem 10.8: If a quadrilateral is inscribed in a circle, then its opposite angle are supplementary.
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EXAMPLE
Quadrilateral QRTS is inscribed in M. If = 87 and = 102. Find and .
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HOMEWORK
Page 549 #8, 10, 14 – 30 Even
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LESSON PLAN
Intro Add a new angle inside a circle, an inscribed
angle. Then develop theorems about inscribed angles.
Standards- 9. Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a
combined review of 10.3 and 10.4 and a quiz. Day 1:
Essential Questions- slides 2 Input-slides 3, 6, 9 – 11, 13 Guided Practice - slides 4, 5, 7, 8, 12, 14 Independent Practice – Book Work