Download Geometry Chapter 6

6.1 Inequalities and Indirect
Proofs
Up until now we have dealt with sides
and angles that are ___________ and
have used the properties of _________
in our proofs.
Now we will deal with _________ sides
and angles. We will be using properties
of ______________.
Property of Inequality
(All of these)
Exterior Angle Theorem: ____________
__________________________________
__________________________________
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2
1
3
Given : AC  BC; CE  CD
Prove : AE  BD
E
B
C
A
D
D
Given : 1 is and exterior angle
Prove : 1  D; 1  E
1
E
F
4
Given : 2> 1
Prove : 2  4
3
1
2
6.3 Indirect Proof
We will be using __________________
_____________________________.
Lets look at an example.
Lets suppose after walking home, Joe
enters the house carrying a dry umbrella.
You can conclude that it is not raining
outside. Why?
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________________________________
Steps for solving an Indirect Proof:
•_________________________________
__________________________________
•_________________________________
__________________________________
•_________________________________
__________________________________
__________________________________
__________________________________
Lets try one, these will be written as a
paragragh.
S
Given : SRQP is a trapezoid
R
Prove: PQ  SR
P
Q
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6.4
Inequalities
Inequalities for one Triangle
Theorem 6.2:
__________________________
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Theorem 6.3:
__________________________
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B
List angles from Largest to
smallest:
10
12
____ ____ ____
C
A
18
A
61
C
60
List sides from Largest to
smallest:
____ ____ ____
59
B
Corollary 1: ______________________________
________________________________________
________________________________________
Theorem 6.4:
___________________________
________________________________________
________________________________________
When given 2 sides of a triangle you can find a
range that the third side will be between.
•_____________________________________
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10,12, ________
25, 26, ________
y, y  2, _______
Find out if each is a triangle, given the sides:
1. 6,8,20
2. 2.5, 5, 4.1
3. 3, 4, 5
4. 6, 4, 2
5. 6, 5, 6
B
Which side is the
longest?
80
C
x
x-10
A
C
59 61
59
A 61
D
60 60
B
____  ____  ____  ____  ____
6.5 Inequalities for 2 Triangles
Theorem 6-5: SAS Inequality
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A
55
B
34
Theorem 6-5: SSS Inequality
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34
55
A
B
Example:
Given : RS  RT ; 1 
What can you deduce?
•____________
R
•____________
_____________
_____________
_____________
2
S
1
2
V
T
Example:
Given : Marked on Drawing
What can you deduce?
S
12
•______________
V
R
X
•______________
14
T
Y
Example:
Given : Marked on Drawing
What can you deduce?
10
1
•______________
5
6
2
•______________
10