Hubarth Geometry 107 Measure of an Inscribed Angle C A B D Ex 1 Use Inscribed Angles a m T mQR b Find the indicated measure in P M T mRS ID: 485648
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Slide1
10.4 Use Inscribed Angles and Polygons
Hubarth
GeometrySlide2
10.7 Measure
of an Inscribed Angle
.
C
A
B
DSlide3
Ex 1 Use Inscribed Angles
a.
m
T
mQR
b.
Find the indicated measure in
P
.
M T =
mRS
=
(48
o
) = 24
o
a.
mQR
= 180
o
mTQ
= 180
o
100
o
= 80
o
. So,
mQR
= 80
o
.
–
–
mTQ
= 2
m
R
= 2
50
o
= 100o. Because TQR is a semicircle,
b.Slide4
Find
mRS
and
m
STR. What do you notice about STR and
RUS?
From
Theorem
10.7,
you know that
mRS
= 2
m RUS
= 2 (31
o
) = 62
o
.
Also
,
m
STR
=
mRS
=
(
62
o
) = 31
o
.
So
, STR RUS.
Ex 2 Find the Measure of an Intercepted ArcSlide5
Theorem 10.8
If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
A
B
C
DSlide6
Ex 3 Standardized Test PracticeSlide7
Inscribed and Circumscribed
If all the vertices of a polygon lie on a circle, the polygon is
inscribed
in the circle and the circle is circumscribed about the polygon. The polygon is an inscribed polygon and the circle is a circumscribed circle.
Inscribed
triangle
Inscribed
Quadrilateral
Circumscribed
Circle
Theorem
10.9
Words If a triangle inscribed in a circle is a right triangle, then the hypotenuse
is a diameter of the circle.
If a side of a triangle inscribed in a circle is a diameter of the circle, then the
triangle is a right triangle
A
B
CSlide8
Theorem
10.10
Words If a quadrilateral can be inscribed in a circle then its opposite angles
are supplementary.
If the opposite angles of a quadrilateral are supplementary, then the quadrilateral can be inscribed in a circle.
.
C
E
F
D
GSlide9
Find the value of each variable.
a.
75
o
+
y
o
= 180o
y = 105
80o + xo = 180o
x = 100
Ex 4 Use Theorem 10.10
b.
2
a
o
+ 2
a
o
= 180
o
a
= 45
4
b
o
+ 2
b
o
= 180
o
b
= 30
4
a
= 180
6
b
= 180Slide10
Practice
Find the measure of the red arc or angle.
1.
5
.
2.
3.
Find the value of each variable.
4
.
6.
x = 100
y = 105
a = 45
b = 30
x = 98
y = 112