10.1 angles in circles
TRANSCRIPT
![Page 1: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/1.jpg)
10.1 Angles in Circles
1
March 24, 2014
Circle Geometry10.1 Exploring Angles in a Circle
![Page 2: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/2.jpg)
10.1 Angles in Circles
2
March 24, 2014
Anatomy of a Circle
What do we know about a circle?
![Page 3: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/3.jpg)
10.1 Angles in Circles
3
March 24, 2014
Anatomy of a Circle
Chord: A line segment with both endpoints on a circle
![Page 4: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/4.jpg)
10.1 Angles in Circles
4
March 24, 2014
Anatomy of a Circle
Central Angle: An angle formed by two radii of a circle.
![Page 5: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/5.jpg)
10.1 Angles in Circles
5
March 24, 2014
Anatomy of a Circle
Inscribed Angle: An angle formed by two chords that share a common endpoint
![Page 6: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/6.jpg)
10.1 Angles in Circles
6
March 24, 2014
Anatomy of a Circle
Arc (of a circle): A portion of the circumference
![Page 7: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/7.jpg)
10.1 Angles in Circles
7
March 24, 2014
Properties of Angles
The inscribed angles subtended by the same arc are congruent.
![Page 8: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/8.jpg)
10.1 Angles in Circles
8
March 24, 2014
Tips and Tricks
If you see a bow tie, you have sets of inscribed angles.
![Page 9: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/9.jpg)
10.1 Angles in Circles
9
March 24, 2014
Properties of Angles
The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.
B
A
C
O
![Page 10: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/10.jpg)
10.1 Angles in Circles
10
March 24, 2014
Tips and Tricks
If you see a Star Trek insignia, you have a set of inscribed angles and central angles.
![Page 11: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/11.jpg)
10.1 Angles in Circles
11
March 24, 2014
ExampleFind ∠ACD and ∠AOD if ∠ABD is 35˚
![Page 12: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/12.jpg)
10.1 Angles in Circles
12
March 24, 2014
ExampleFind ∠ACD and ∠AOD if ∠ABD is 35˚
![Page 13: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/13.jpg)
10.1 Angles in Circles
13
March 24, 2014
Properties of Angles
Angles inscribed in a semicircle are right angles.
![Page 14: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/14.jpg)
10.1 Angles in Circles
14
March 24, 2014
ExamplePoint C is the centre of the circle. The diameter AB is 10cm and the chord BD is 6 cm. B
D
C
A
![Page 15: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/15.jpg)
10.1 Angles in Circles
15
March 24, 2014
Example
Determine the measure of the missing angle
![Page 16: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/16.jpg)
10.1 Angles in Circles
16
March 24, 2014
Example
Determine the measure of angle y
![Page 17: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/17.jpg)
10.1 Angles in Circles
17
March 24, 2014
![Page 18: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/18.jpg)
10.1 Angles in Circles
18
March 24, 2014
Example
Determine the measure of the missing angles
![Page 19: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/19.jpg)
10.1 Angles in Circles
19
March 24, 2014
Example
Determine the measure of the missing angles
![Page 20: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/20.jpg)
10.1 Angles in Circles
20
March 24, 2014
Example
Determine the measure of the missing angle
![Page 21: 10.1 Angles in Circles](https://reader033.vdocuments.site/reader033/viewer/2022052410/5559cc1dd8b42a93208b48b4/html5/thumbnails/21.jpg)
10.1 Angles in Circles
21
March 24, 2014
Questions page 3823, 4, 10, 12, 20a