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Geometry
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.
Vocabulary
Definition
Illustrations
An inscribed angle is an angle whose
Inscribed Angle
____________ is on a circle and
whose sides contain ________ of the
circle.
The arc that lies in the interior of an
_______________ angle and has
Intercepted Arc
_______________ on the angle is
called the intercepted arc of the
angle.
Inscribed Polygon
A polygon is an inscribed polygon if all
of its ______________ lie on a circle.
A circumscribed circle is a circle that
Circumscribed Circle
contains the vertices of an
______________ polygon.
MEASURE OF AN INSCRIBED ANGLE THEOREM
The measure of an inscribed angle is one half the measure of its____________________________.
mADB = ½ • _________
1) Find the indicated measure in P.
a) mS
b) Measure of arc RQ.
2) Find the measure of arc HJ and HGJ. What do you notice about HGJ and HFJ?
If two inscribed angles of a circle intercept the same arc, then the angles are _____________.
ADB  _________
3) Name two pairs of congruent angles in the figure.
4) Find the indicated measure.
a) mGHJ
b) Measure of arc CD
c) mRTS
If a _________ triangle is inscribed in a circle, then the ____________is a diameter of the circle.
Conversely, if one side of an inscribed triangle is a ________________ of the circle, then the
triangle is a ___________ triangle and the angle opposite the diameter is the___________ angle.
mABC = 90 if and only if ______ is a diameter of the circle.
A quadrilateral can be inscribed in a circle if and only if its opposite angles are_______________.
D, E, F, and G lie on C if and only if mD + mF = mE + mG = ________.
5) Find the value of each variable.
a)
b)
c)
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