Geometry
Notes
Name_________________________
Using Inequalities in One and Two Triangles
Example 1
Draw an obtuse scalene triangle. Find the largest angle and the longest side and label them. Then
find the smallest angle and the shortest side and label them. What do you notice?
Longer Side Concept
Larger Angle Concept
B
8
B
5
50
A
C
30
A
C
Example 2
List the sides of RST in order from shortest to longest.
S
121
29
R
Example 3
30
T
Triangle Inequality TheoremThe sum of the lengths of any two sides of a triangle is greater than the length of the third side.
B
AB + BC > AC
AC + BC > AB
AB + AC > BC
A
Example 3
a. A triangle has one side length of 12 and another of length 8. Describe the possible lengths of the
third side.
b. A triangle has one side length of 26 and another of length 19. Describe the possible lengths of the
third side.
Example 4
Can the following three side lengths form a triangle?
a. 1, 2, 3
b. 2, 2, 3
c. 2, 2, 2
Example 5
a. Describe the possible distance from Granite Peak to Fort Peck Lake
b. List the angles in order from least to
greatest.
Example 6
Describe the possible values of x.
11
13
X+7
Example 7
You are bending a pipe cleaner into an isosceles triangle. The pipe cleaner is 24 inches long and the
first bend is at 10 inches. Draw and label the two isosceles triangles that you could create.
C