x
1
5.5 The Triangle Inequality
By: Jarica Taylor, Eva Cantave, Analisa Samusson
Example 1
Add the two
smallest
sides to see if its greater than the
largest
side.
Find the range of the
third
value.
Example 2
J
l
k
Examples:
kj + jl >kl
jl + kl > kj
kl + kj > jl
11in 9+11= 20
20 > 17
17in
Content Overview
13 in 20in
x in
Example 2
5in
2in
x in
let x represent the third side
solve each of the three inequalities
If the measures of two sides of a triangle are 5 inches and 2 inches, which
is the least possible measure for the third side.
A)13in
B)7in
C) 10in
D)4in
5+ x 2 subtract 5 and 2
add 5 and 2
x + 2 > 5
x> 3
subtract 5 and 2
13 + 20>33
2013= 7
7< x < 33
5 + 2>x
7< x or x >7
Quiz Question
1) Determine the possible value of x ?
x+18
6x+5
4x1
A
E
J
Quiz Question
2)
Find the range for the measure of the third
side of a triangle given the measures of two sides.
4
Real world
Billy cut a huge piece of paper in order to make a triangle to form a pyramid for his world history project. Which of the following side lengths couldn't have been the triangle he had cut out?
add 13 and 20
subtract 20 and 13
the range of values that fit both inequalities is x>3 and x<7, which can be written as 3<x<7
ANSWER!!
9in
A) 15,23,9
B) 35.3,49.1,28
C) 16,17,9
D) 15,30,15
The range of values that fit both inequalities is
x>3 and x<7, which can be written as
3> x <7. Therefore the least whole number value between 3 and 7 is 4. so the correct answer
is D.
ANSWER
Answer
Answer
5.5 Triangular Inequality Theorem:
The sum of the lengths of the smallest two sides of a triangle must be greater than the length of the largest side.
which equals 33
A.
15
+
9
>
23
24
>
23
C.
16
+
9
>
17
B.
35.3
+
28
>
49.1
63.8
>
49.1
25
>
17
D.
15
+
15
>
30
30
>
30
The answer is D because inequalities can not
be equal to each other or have the same number.
3
4
1
3
+9 >x
4
1
3
x
+
+
9
1
3
13
+
27
3
13
1
3
add
40
3
multiply 9 over the common factor , which is 3.
3

13
divide
3
14
3
Subtract
9 ft
x
23
f
4
2
3
3
>
x
<
4
2
3
ANSWER
> x >
Divide
4
2
AJ
+
AE
>
JE
(
x
+18)
+
(4
x
1)
>
(6x+5)
5x17
>
6x+5
add 17 on both sides
+
17
+
17
5x
>
6x+22
6
6
x
AJ
+
JE
>
AE
(x+
18
)+(
6x+5
) > (
4x

1
)
7x+23 >4x1
23
23
7x > 4x 24
4x
4x
3x > 24
3 3
=
x
> 8
1x
1
>22
1
=
x
> 22
simplify
subtract 6 on both sides
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The triangle inequality
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