1. Inequalities in One Triangle
Section 5.5
Inequalities in One Triangle

2. 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

3. 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

4. Write the sides/angles in order from least to greatest.15 33 63 C 32 B F 22 D

5. Is PQ>8? Is RQ<8? Q 57 61 P R 8

6. 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

7. What are the possible angle measures of <A?42 A

8. 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

9. Is it possible to have a triangle with the given side lengths?
3, 8, 3
6, 7, 12
9, 5, 11
8, 12, 20

10. What are the possible lengths of the third side of the triangle?
8, 17, ?
12, 18, ?

11. Write and solve the inequality PQ + QR > PR.
2x+1
3x-3 P R
3x+1