sec 8.3 notes.notebook - ms. shannon bishop's math websitesec 8.3 notes.notebook 2 may 15, 2013...
TRANSCRIPT
sec 8.3 notes.notebook
1
May 15, 2013
sec 8.3 notes.notebook
2
May 15, 2013
Section 8.3 Properties of Angles in a Circle
Central Angle and Inscribed Angle Property
The measure of a central angle is twice the measure of an inscribes angle subtended by the same arc.
x
2x
sec 8.3 notes.notebook
3
May 15, 2013
Examples
#1#2#3
60o
30o
70o
x
y
18o
Since x is half of 70, x = 35o.
Since y is twice 18, y = 2 x 18 = 36o
sec 8.3 notes.notebook
4
May 15, 2013
Inscribed Angles Property
Inscribed angles subtended by the same arc are equal.
2x
x
xx
sec 8.3 notes.notebook
5
May 15, 2013
Examples
#1
y
x
22o
A
BC
D
O
Central and inscribed are both subtended by arc AB
and are inscribed anglessubtended by the same arc AB.So, x = 22o
sec 8.3 notes.notebook
6
May 15, 2013
#2
y
x
14o
A
BC
D
O
Central and inscribed are both subtended by arc AB
and are inscribed anglessubtended by the same arc AB.So, x = 14o
sec 8.3 notes.notebook
7
May 15, 2013
50o
x
y
A
BC
D
O
#3
Since both inscribed angles are subtended from the same arc as the central angle
sec 8.3 notes.notebook
8
May 15, 2013
Angles in a Semicircle Property
Inscribed angles subtended by a semicircle are right angles
90o
90o
90o
sec 8.3 notes.notebook
9
May 15, 2013
Examples # 1
40o
x
y
I
M
O
N
is an inscribed angle subtended bya semicircle.so, x = 90o
Since 3 angles in a triangle add to 180 o,y + 90 + 40 = 180y + 130 = 180y + 130 130 = 180 130y = 50o
sec 8.3 notes.notebook
10
May 15, 2013
60o
x
y
I
M
O
N
Example # 2 Try this one!
is an inscribed angle subtended bya semicircle.so, x = 90o
Since 3 angles in a triangle add to 180 o,y + 90 + 60 = 180y + 150 = 180y + 150 150 = 180 150y = 30o
sec 8.3 notes.notebook
11
May 15, 2013
sec 8.3 notes.notebook
12
May 15, 2013
sec 8.3 notes.notebook
13
May 15, 2013
Practice Pages 410 412#'s 4, 5, 6, 11