1. Triangle Inequalities
Part 2

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.

3. Example

4. Triangle Sides
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.

5. Examples
List the Angles from largest to smallest

6. Triangle Angles
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.

7. Examples
List the sides of triangle from largest to smallest

8. Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Always check using the two smallest sides, they must be larger than the third. If this is true the numbers will represent a triangle.

9. Example Do these numbers represent a triangle? 1.) 9, 7, 12 Yes
2.) 5, 5, 10 No
3.) 1, 4, 6
4.) 6, 6, 2

10. Finding Range of Third Side
If you are given two sides of a traingle you can determine the range that the third side must fall in.
To find the smallest possible side length you subtract the larger side from the smaller side. The value you get can not be a side, however everything larger will work
To find the largest your third side could be you add your two given sides, although this value will not work everything less than it will.

11. Example
If you have two sides of a triangle 4 in and 7 in what is the range for the possible third side, n.
3in < n < 11in
If you have two sides of a triangle 8 in and 12 in what is the range for the possible third side, n.
4in < n < 20in

12. Hinge Theorem
If two sides of one triangle are congruent two two sides of another triangle, and the included angles are not congruent, then the longest side is opposite the larger included angle.

13. Example

14. Converse of the Hinge Theorem
If two sides of one triangle are congruent to two sides of another triangle, and the third sides are not congruent, then the larger included angle is opposite the longer third side.

15. Example