1. Triangle Inequality Theorems Sec 5.5 Goals: To determine the longest side and the largest angle of a triangle To use triangle inequality theorems

2. Longest and shortest sides of a triangle Shortest side Largest angle Smallest angle Longest side

3. 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.

4. 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.

5. Exterior Angle Inequality Theorem 5.12 The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles.

6. Triangle Inequality Theorem 5.13 The sum of the lengths of any two sides of a triangle is greater that the length of the third side.

7. Example A triangle has one side equal to 8 cm and another side equal to 17cm. Describe the possible lengths of the third side.

8. Example Which of the following triangles are possible to construct? 3 in, 3 in, 8 in 6 in, 6 in, 12 in 4 in, 4 in, 4 in 9 in, 5 in, 11 in

9. Example Fill in the appropriate symbol:, =