5.5 Inequalities in One
Triangle
Order of sides in a triangle
The largest side of a triangle is across from
the largest angle; the smallest side is
across from the smallest angle.
A
B
C
IfAC  AB, thenB  C
Conversely
IfA  B, thenBC  AC
The largest angle of a triangle is across from
the largest side; the smallest angle is
across from the smallest side.
A
B
C
Another Theorem about
Inequalities
Remember that an exterior angle is the sum
of the remote interior angles, then the next
theorem should not be surprising.
An outside angle is greater then either of the
remote interior angles. m1  m2  m3
So
2
3
1
m1  m2
m1  m3
Christmas wrapping principle
When wrapping a flat object, you need to
have enough paper to make a triangle
over the top.
The sum of any two sides of a triangle is
greater then the third side.
Write the angles in order
then the sides
B
111
48
C
23
A
Write the sides in order
then the angles
U
7
10
T
11
R
Can these sides be sides of a
triangle?
#1. 3, 3, 8
#2. 6, 6, 12
#3. 9, 5, 11
What is the possible values for the
last side?
A triangle have one side of 8 and another of
17, what are the possible of the third side.
Greater then
But
Less then
Homework
Page 298
# 6 - 23
Homework
Page 299 – 301
# 24 – 31,
42 - 45