10.2– find arc measures. termdefinitionpicture central angle an angle whose vertex is the center...
TRANSCRIPT
10.2– Find Arc Measures
Term Definition Picture
Central Angle
An angle whose vertex is the center of the circle
P
A
C
APC
Term Definition Picture
Minor Arc
Arc of a circle that is less than 180°
P
A
C
ACªTwo letters:
Term Definition Picture
Major Arc
Arc of a circle that is more than 180°
P
A
C
ABCº3 letters:
B
Term Definition Picture
Semicircle
Arc of a circle that is 180°
P
A
C
ABCº3 letters:
B
Term Definition Picture
Congruent circles
Two circles with the same radius
Term Definition Picture
Congruent arcs
Arcs that have the same central angle
A B
CD
ABª CDª
The measure of a minor arc is the measure of its _____________ angle.central
P
A
Cx°
x°
MNº
73°
73°
73°
minor
NQª
73°107°
26°minor
MPº
73°154°
26°minor
MRPº
73°206°
26°
107°
major
PNª
73°81°
26°
107°
minor
MNQº
73°180°
26°
107°
semicircle
MRQº
73°180°
26°
107°
Semicircle
MRNº
73°287°
26°
107°
major
10.4 – Use Inscribed Angles and Polygons
An angle whose vertex is on a circle and whose sides are chords of the circle
Inscribed angle:
An arc that is inside an inscribed angle
Intercepted Arc:
A polygon that has all of its vertices on a circle
Inscribed Polygon :
The circle that contains the vertices of a polygon
Circumscribed Circle:
The measures of an inscribed angle is ________ the measure of its ______________ arc.
halfintercepted
D = AB 2
x°
2x°
If two inscribed angles of a circle _____________ the same arc, then the angles are _____________.
interceptcongruent
D C
A ________ triangle is inscribed in a circle iff the _______________ is a diameter of the circle.
righthypotenuse
B is a right angle because it inscribes a semicircle.
A ____________________ can be inscribed in a circle iff its opposite angles are ______________.
quadrilateralsupplementary
mD + mF = 180°
mE + mG = 180°
Find the indicated measure.
=158 2
= 79°
Find the indicated measure.
=180 2
= 90°
180°
90°
Find the indicated measure.
= 40 2 = 80°
Find the indicated measure.
=
88°
92°
92 2
= 46°
Find the indicated measure.
=80 2
= 40°100°
80°
Find the indicated measure.
=56 2
= 28°
56°
Find the measure of A and C.
80°
mA =80 2
= 40°64°
mC =64 2
= 32°
Find the measure of A and C.
mA =146 2
= 73°
mC =62 2
= 31°
146°
62°
mPNO = 68 2
= 34°
mQNP = 62 2
= 31°
62°
= 62°
62°
= 130°
62°
= 112°
62°
112°
= 248°
62°
112°
Decide whether a circle can be circumscribed about the figure.
70 + 130 180
No,
Decide whether a circle can be circumscribed about the figure.
91 + 89 = 180
Yes,
91°
Decide whether a circle can be circumscribed about the figure.
115 + 63 180
No,
Find the value of the variables.
5x + 110 = 180
5x = 70
x = 14°
2y + 104 = 180
2y = 76
y = 38°
Find the value of the variables.
x + 108 = 180
x = 72°
y + y = 180
2y = 180
y = 90°
Find the value of the variables.
4x = 84+44 2
8x = 128
x = 16°
7y = 152+44 2
14y = 196
y = 14°
44°
1 1
Find the value of the variables.
12x = 96+48 2
24x = 144
x = 6°
3y = 48+171 2
6y = 219
y = 36.5°
171°
1 1
10.210.4
662-663676-679
3-12, 16, 17, 22, 233-8, 11-15 odd, 16, 18
HW Problem
10.4 #15
3a = 54+66 2
6a = 120
a = 20°
4b = 66+110 2
8b = 176
b = 22°
66°1 1