1. 5-2 Inequalities and Triangles
Definition of Inequality
For any real numbers a and b, a > b if and only if there is a positive number c such that a = b + c

2. Review of the Symbols = Not equal to > Greater than or equal to
< Less than or equal to
> Not greater than or equal to
< Not less than or equal to

3. Review of the Properties
Comparison Property: a < b, a = b, or a > b
Transitive Property:
If a < b and b < c, then a < c
If a > b and b > c, then a > c
Addition and Subtraction Properties
If a > b, then a + c > b + c, and a – c > b – c
If a < b, then a + c < b + c, and a – c < b – c
Multiplication and Division Properties
If c > 0, and a < b, then ac < bc and a/c < b/c
If c > 0, and a > b, then ac > bc and a/c > b/c
If c < 0, and a < b, then ac > bc and a/c > b/c
If c < 0, and a > b, then ac < bc and a/c < bc

4. Exterior Angle Review
Exterior angle – forms a linear pair with one of the angles of a triangle.
Example: 2 &6… 2 & 5
Remote interior angles – the two angles that do NOT form a linear pair with the exterior angle.
Example: 5 with 1 & 3 6 2 5 7 3 8 1 4 9

5. Theorem 5.8
82° 1 3 2
Exterior Angle Inequality Theorem – If an angle is an exterior angle of a triangle, then its measure is greater than the measure of either of its corresponding remote interior angles.
Name two angles in ΔCDE that have a measure less than 82°.
2 and 3
Try #2 Check your Progress on page 282
5 and 6

6. Theorem 5.9
If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
Greater Measure
Longer Side

7. Theorem 5.10
If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.
Greater Measure
Longer Side

8. Try these – page 284 #1-9 Homework #32
P , (x 3’s), 40-42, 50, 52