The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

1
The positions of the longest and shortest sides
of a triangle are related to the positions of the
largest and smallest angles.
2
Example 1 Ordering Triangle Side Lengths and
Angle Measures
Write the angles in order from smallest to
largest.
The angles from smallest to largest are ?F, ?H
and ?G.
3
Example 2 Ordering Triangle Side Lengths and
Angle Measures
Write the sides in order from shortest to longest.
m?R 180 (60 72) 48
48
4
Example 3
5
Example 4
6
A triangle is formed by three segments, but not
every set of three segments can form a triangle.
7
A certain relationship must exist among the
lengths of three segments in order for them to
form a triangle.
NOTE Just check that the sum of the two shorter
sides is greater than the longest side.
8
Example 5 Applying the Triangle Inequality
Theorem
9
Example 5 Applying the Triangle Inequality
Theorem
10
Example 6 Finding Possible Side Lengths
The lengths of two sides of a triangle are 8
inches and 13 inches. Find the range of possible
lengths for the third side.
Let x represent the length of the third side.
Then apply the Triangle Inequality Theorem.
x 8 gt 13
8 13 gt x
x gt 5
21 gt x
Combine the inequalities. So 5 lt x lt 21. The
length of the third side is greater than 5 inches
and less than 21 inches.
11
Example 7
The lengths of two sides of a triangle are 22
inches and 17 inches. Find the range of possible
lengths for the third side.
12
You can also use side lengths to classify a
triangle as acute or obtuse.
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)