Download H>Jt I Use Inscribed Angles and Polygons

Geometry Lesson 10-4: Use Inscribed Angles and Polygons
Learning Target: By the end of today’s lesson we will be able to successfully use inscribed angles of circles.
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Inscribed angle: _____________________________________________________________________
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Intercepted arc: _____________________________________________________________________
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Inscribed polygon: __________________________________________________________________
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Circumscribed circle: ________________________________________________________________
Theorem 10.7: Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is one half the measure of its intercepted arc.
mADB = ½ • ___________
Example 1: Find the indicated measure in P.
a.) mS
b.) measure of arc RQ.
Example 2: Find the measure of arc HJ and HGJ.
What do you notice about HGJ and HFJ?
Theorem 10.8:
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
ADB  ___________
Example 3: Name two pairs of congruent angles in the figure.
Example 4: Find the indicated measure.
a.) mGHJ
b.) measure of arc CD
c.) mRTS
Theorem 10.9:
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.
mABC = 90 if and only if ______ is a diameter of the circle.
Example 5: A security camera rotates 90 and needs to be able to view the width of a wall.
The camera is placed in a spot where the only thing viewed when rotating is the
wall. You want to change the camera’s position. Where else can it be placed so
that the wall is viewed in the same way?
Theorem 10.10:
A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.
D, E, F, and G lie on C if and only if mD + mF = mE + mG = ________.
Example 6: Find the value of each variable.
a.)
b.)
c.)