6.1 Inequalities and Indirect Proofs
Jan 03, 2016
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: ____________
__________________________________
__________________________________
__________________________________
1
2
3
: ;
Prove :
Given AC BC CE CD
AE BD
A
B
C
D
E
: 1 is and exterior angle
Prove : 1 ; 1
Given
D E
F
D
E
1
: 2> 1
Prove : 2 4
Given
1
3
2
4
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?
________________________________
________________________________
Steps for solving an Indirect Proof:
•___________________________________________________________________
•___________________________________________________________________
•_______________________________________________________________________________________________________________________________________
Lets try one, these will be written as a paragragh.
: is a trapezoid
Prove: PQ SR
Given SRQP
S R
P Q
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6.4
Inequalities
Inequalities for one Triangle
Theorem 6.2: __________________________
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________________________________________
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Theorem 6.3: __________________________
________________________________________
________________________________________
________________________________________
A
B
C
10 12
18
List angles from Largest to smallest:
____ ____ ____
61
60 59
A
BC
List sides from Largest to smallest:
____ ____ ____
Corollary 1: ______________________________
________________________________________
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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.
•_____________________________________
______________________________________
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10,12, ________
25,26, ________
, 2, _______y y
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
80
x x-10
B
AC
Which side is the longest?
A
B
C
D61
59
60
61
60
59
____ ____ ____ ____ ____
6.5 Inequalities for 2 Triangles
Theorem 6-5: SAS Inequality
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55 34
A B
Theorem 6-5: SSS Inequality
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55 34
A B
Example:
What can you deduce?
: ; 1 2Given RS RT
1
2R
T
V
S
•____________
•___________________________________________________
Example:
What can you deduce?
: Marked on DrawingGiven
R
T
V
S
•______________
•______________
Y
X
12
14
Example:
What can you deduce?
: Marked on DrawingGiven
5
10
•______________
•______________10
1
6
2