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50.
Sample answer: The length of any side of a
triangle is greater than the differences between
the lengths of the other two sides.
Paragraph Proof:
By the Triangle Inequality Theorem, for
n
ABC
with side measures
a
,
b
, and
c
,
a
1
b
.
c
,
b
1
c
.
a
, and
c
1
a
.
b
.Using the Subtraction
Property of Inequality,
a
.
c
2
b
,
b
.
a
2
c
, and
c
.
b
2
a
.
51.
Sample answer: You can use the Triangle
Inequality Theorem to verify the shortest route
between two locations. Answers should include
the following.
• A longer route might be better if you want to
collect frequent flier miles.
• A straight route might not always be available.
52.
D; If the perimeter is 29, the measure of the third
side is 10.
7
1
10
¬
.
?
12
7
1
12
¬
.
?
10
10
1
12
¬
.
?
7
17
¬
.
12
✓
19
¬
.
10
✓
22
¬
.
7
✓
So, 7, 12, and 10 could be the sides of a triangle
with perimeter 29.
If the perimeter is 34, the measure of the third
side is 15.
7
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.
 Fall '10
 Dr.Zhan
 Calculus, PreCalculus

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