1. 5-2 Inequalities and Triangles
Students will recognize and apply properties of inequalities to the measure of angles and sides of a triangle.
S. Calahan
2008

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

3. 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 interior angles.
m<4 > m<1
m<4 > m<2 B 2 1 3 A 4 C

4. Exterior Angle Inequality Theorem
Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition All angles that are less
than m<4. B
m>4 > m<5
m>4 > m>6
m>4 > m>2
m>4 > m>1 +m>5 2 7 6 1 5 3 A 4 C

5. Angle-Side Relationship
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.
order from least to
greatest according to the <s B 10 8
<B, <C, <A A 6 C

6. Side-Angle Relationship
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.
arrange least to greatest
according to the sides B 30
AC, AB, BC 60 C A