unit 6: circles and circular functions lesson 1: properties of ......2014/12/17 · lesson 1:...
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Unit 6: Circles and Circular Functions
Lesson 1: Properties of Circles
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Unit 6Circles
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Investigation 1
Tangents to a Circle
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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
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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
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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
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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.
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a) b) c)
Example:
pg. 408 # 3
P
A
B
10 in. 18 in.
P
A
B
10 in.
a)
b)
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1) 2)
3) 4)
5)
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Investigation 2
Chords, Arcs, and Central Angles
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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
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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?
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3
8.9 4.6
8.1 5.2
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11.4 9.4
6.1 6.3
9.4 7.1
9.9 8.4
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Investigation 3
Angles Inscribed in a Circle
http://www.mathopenref.com/circleinscribed.html
Let's take a look at inscribed angles
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