unit 6: circles and circular functions lesson 1: properties of ......2014/12/17 · lesson 1:...
Post on 19-Jun-2021
2 Views
Preview:
TRANSCRIPT
Unit 6 Lesson 1.notebook
1
December 17, 2014
Unit 6: Circles and Circular Functions
Lesson 1: Properties of Circles
Unit 6 Lesson 1.notebook
2
December 17, 2014
Unit 6 Lesson 1.notebook
3
December 17, 2014
Unit 6Circles
Unit 6 Lesson 1.notebook
4
December 17, 2014
Investigation 1
Tangents to a Circle
Unit 6 Lesson 1.notebook
5
December 17, 2014
Unit 6 Lesson 1.notebook
6
December 17, 2014
Unit 6 Lesson 1.notebook
7
December 17, 2014
Unit 6 Lesson 1.notebook
8
December 17, 2014
Unit 6 Lesson 1.notebook
9
December 17, 2014
O
Draw a tangent line touching the circle at Point A. Point A is called the point of tangency.
Draw segment OA. Relative to the radius, how long is OA? ___________
Suppose B is any point on the tangent line other than A. Relative to r, how long is OB? _________
Find the measure of the angle made by OA and the tangent line. Write a conjecture about a tangent line and the radius drawn to the point of tangency.
Is the converse of your conjecture also true? If so, write your conjecture in ifandonlyif form.
Page 398 #1
0o
Unit 6 Lesson 1.notebook
10
December 17, 2014
Tangent Theorem
If a line is tangent to a circle, then the line is _________________ to a radius of the circle drawn to the point of tangency.
pg. 399 # 3
perpendicular
A B
o
Unit 6 Lesson 1.notebook
11
December 17, 2014
Name: ______________________________________________Write a twocolumn proof using the information given. Be careful, the information is out of order and some things may be missing entirely.
Statement Reason
Given
PR = PT All Radii are =
PRS = 90
PTS = 90Circle Tangent Prop.
SP = SP Reflexive Prop
Unit 6 Lesson 1.notebook
12
December 17, 2014
Statement Reason
Given
Tangent and radius are perpendicular
Definition of a circle
Definition of congruence
SP SP = Reflexive Property
HL Congruence Theorem
CPCTC
Name: ______________________________________________Write a twocolumn proof using the information given. Be careful, the information is out of order and some things may be missing entirely.
Unit 6 Lesson 1.notebook
13
December 17, 2014
a) b) c)
Example:
pg. 408 # 3
P
A
B
10 in. 18 in.
P
A
B
10 in.
a)
b)
Unit 6 Lesson 1.notebook
14
December 17, 2014
1) 2)
3) 4)
5)
Unit 6 Lesson 1.notebook
15
December 17, 2014
Unit 6 Lesson 1.notebook
16
December 17, 2014
Investigation 2
Chords, Arcs, and Central Angles
Unit 6 Lesson 1.notebook
17
December 17, 2014
Unit 6 Lesson 1.notebook
18
December 17, 2014
Unit 6 Lesson 1.notebook
19
December 17, 2014
Unit 6 Lesson 1.notebook
20
December 17, 2014
Unit 6 Lesson 1.notebook
21
December 17, 2014
Read pg. 401 Use it to help you complete the following statements about circle P:
P
Q
R
Angle RPQ is called the __________________ angle, and it measures less than 180 degrees.
RQ is called a _____________________ .
S
RSQ is called a ______________ arc and it is equal _____ minus the measure of _________________ .
RQ is called a _______________ arc and it is equal to the measure of the ______________________ .
If RQ is equal to 120 degrees,
What is the measure of RSQ? _________
What is the measure of the central angle? _____________
Answer pg. 401 # 1 below:
a)
b)
c)
A
B
CD
O
pg. 402 # 2
a) Statement Reason b) Statement Reason
c) The measures of two minor arcs are equal if and only if
Unit 6 Lesson 1.notebook
22
December 17, 2014
Unit 6 Lesson 1.notebook
23
December 17, 2014
Unit 6 Lesson 1.notebook
24
December 17, 2014
Unit 6 Lesson 1.notebook
25
December 17, 2014
Unit 6 Lesson 1.notebook
26
December 17, 2014
Construct a radius perpendicular to chord AB. Label the point of intersection X.
P
Draw chord AB.
Measure AX and BX, what do you observe?
Unit 6 Lesson 1.notebook
27
December 17, 2014
3
8.9 4.6
8.1 5.2
Unit 6 Lesson 1.notebook
28
December 17, 2014
11.4 9.4
6.1 6.3
9.4 7.1
9.9 8.4
Unit 6 Lesson 1.notebook
29
December 17, 2014
Investigation 3
Angles Inscribed in a Circle
http://www.mathopenref.com/circleinscribed.html
Let's take a look at inscribed angles
Unit 6 Lesson 1.notebook
30
December 17, 2014
Unit 6 Lesson 1.notebook
31
December 17, 2014
Unit 6 Lesson 1.notebook
32
December 17, 2014
Unit 6 Lesson 1.notebook
33
December 17, 2014
Unit 6 Lesson 1.notebook
34
December 17, 2014
Unit 6 Lesson 1.notebook
35
December 17, 2014
Unit 6 Lesson 1.notebook
36
December 17, 2014
Unit 6 Lesson 1.notebook
37
December 17, 2014
Unit 6 Lesson 1.notebook
38
December 17, 2014
Unit 6 Lesson 1.notebook
39
December 17, 2014
Unit 6 Lesson 1.notebook
40
December 17, 2014
top related