6.1 Inequalities and Indirect Proofs

1
6.1 Inequalities and Indirect Proofs
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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 ______________.
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Property of Inequality (All of these)
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Exterior Angle Theorem ____________ ____________
______________________ ___________________________
_______ __________________________________
5
E
B
C
A
D
6
D
1
E
F
7
4
3
1
2
8
6.3 Indirect Proof
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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
• __________________________________________________
  _________________
• __________________________________________________
  _________________
• __________________________________________________
  __________________________________________________
  ___________________________________

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Lets try one, these will be written as a
paragragh.
S
R
Q
P
__________________________________________ _______
___________________________________
__________________________________________ ______
____________________________________ _____________
_____________________________ ____________________
______________________
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6.4 Inequalities
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Inequalities for one Triangle
Theorem 6.2 __________________________ __________
______________________________ ___________________
_____________________ ____________________________
____________ Theorem 6.3 _______________________
___ ________________________________________ _____
___________________________________ ______________
__________________________
14
B
List angles from Largest to smallest ____
____ ____
10
12
A
C
18
A
List sides from Largest to smallest ____ ____
____
61
60
59
B
C
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Corollary 1 ______________________________ _____
___________________________________ ______________
__________________________ Theorem 6.4
___________________________ ______________________
__________________ _______________________________
_________
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• When given 2 sides of a triangle you can find a
  range that the third side will be between.
• _____________________________________
• ______________________________________
• ______________________________________

17

• Find out if each is a triangle, given the sides
• 6,8,20
• 2.5, 5, 4.1
• 3, 4, 5
• 6, 4, 2
• 6, 5, 6

18
B
Which side is the longest?
80
x
x-10
A
C
19
C
59
61
D
59
A
61
60
60
B
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6.5 Inequalities for 2 Triangles
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Theorem 6-5 SAS Inequality _____________________
__________________________________________________
__________________________________________________
__________________________________________________
__________________________________________________
_
A
B
55
34
22
Theorem 6-5 SSS Inequality _____________________
__________________________________________________
__________________________________________________
__________________________________________________
__________________________________________________
_
34
55
A
B
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Example What can you deduce?
S

• ____________
• __________________________________________________
  _

1
V
R
2
T
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Example What can you deduce?
S
12

• ______________
• ______________

V
R
X
14
T
Y
25
Example What can you deduce?
10
1

• ______________
• ______________

5
6
2
10