10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex...
-
Upload
tabitha-haynes -
Category
Documents
-
view
212 -
download
0
Transcript of 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex...
![Page 1: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/1.jpg)
10.4 Inscribed Angles
5/7/2010
![Page 2: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/2.jpg)
Using Inscribed Angles• An inscribed
angle is an angle whose vertex is on a circle and whose sides contain chords of the circle.
• Intercepted arc is an arc that lies in the interior of an inscribed angle and has endpoints on the angle.
intercepted arc
inscribed angle
![Page 3: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/3.jpg)
To find the measure of an arc use the central angle.
Central angle
115˚
115˚
![Page 4: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/4.jpg)
Theorem 10.7: Measure of an Inscribed Angle
• If an angle is inscribed in a circle, then its measure is one half the measure of its intercepted arc.
mADB = ½mAB
A
D
B
130˚
(½)130 = 65˚
![Page 5: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/5.jpg)
Ex. 1: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.
Q
RS
T
QTSm = 2mQRS =
2(90°) = 180°
![Page 6: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/6.jpg)
m = 2mZYX =
Ex. 2: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.
ZWX
2(115°) = 230°
XY
Z
W
115˚
![Page 7: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/7.jpg)
m = ½ m
Ex. 3: Finding Measures of Arcs and Inscribed Angles
• Find the measure of the blue arc or angle.NMP
½ (100°) = 50°
NP
P
N
M
100°
![Page 8: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/8.jpg)
Theorem 10.8
• If two inscribed angles of a circle intercept the same arc, then the angles are congruent.
• C D
C
B
A
D
![Page 9: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/9.jpg)
Ex. 4: Finding the Measure of an Angle
• It is given that mE = 75°. What is mF?
• E and F both intercept , so E F. So, mF = mE = 75°
GH
H
G
E
F
75°
![Page 10: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/10.jpg)
Example
68/2 = 34
180-118 = 62
62/2 = 31
62 + 68 = 130
180-68 = 118 118 + 62 = 180
Same as arc QP=62
68 + 62 + 118 = 248
![Page 11: 10.4 Inscribed Angles 5/7/2010. Using Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the.](https://reader035.fdocuments.in/reader035/viewer/2022072013/56649e725503460f94b708f5/html5/thumbnails/11.jpg)
Assignment
• Practice Workbookp. 193(1-15)