### Theorem 5.10 - Belle Vernon Area School District

```Section 5.5
Inequalities in One Triangle
Theorem 5.10
• If one side of a triangle is longer than
another side, then the angle opposite the
longer side is larger than the angle
opposite the shorter side.
15
B
12
A
A  B
THEOREM 5.11
• If one angle of a triangle is larger than
another angle, then the side opposite the
larger angle is longer than the side
opposite the smaller angle
60 o
Side 2
Side 1 > Side 2
45 o
Side 1
Write the sides/angles in order
from least to greatest.
A
E
15
33
63
C
32
B
F
22
D
Is PQ>8? Is RQ<8?
Q
57
61
P
8
R
Exterior Angle Inequality
• The measure of an exterior angle of a
triangle is greater then the measure of
either of the two nonadjacent interior
angles.
A
1
B
<1 is greater than <A
<1 is greater than <B
What are the possible angle
measures of <A?
42
A
Triangle Inequality
• The sum of the lengths of any two sides of
a triangle is greater than the length of the
third side.
A
AB + BC >AC
AC + BC > AB
AB + AC > BC
C
B
Is it possible to have a triangle
with the given side lengths?
• 3, 8, 3
• 6, 7, 12
• 9, 5, 11
• 8, 12, 20
What are the possible lengths of
the third side of the triangle?
• 8, 17, ?
• 12, 18, ?
Write and solve the inequality
PQ + QR > PR.
Q
2x+1
3x-3
P
3x+1
R
```