1. Lesson 5.5 Use Inequalities in a Triangle

2. Theorem 5.10 A B C 8 5 IF AB > BC, THEN C > A The angle opposite the longest side is the largest angle; pattern continues for the smallest and middle length sides.

3. Theorem 5.11 A B C 50ᵒ30ᵒ m A > m C, so BC > AB The side opposite the biggest angles is the biggest side; pattern continues for the smallest and middle measures of angles.

4. Theorem 5.12 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the third side. This theorem is used to make a prediction of the possible lengths of the third side. In other words to find the maximum length and minimum length. Therefore one of the three inequalities will be eliminated – Eliminate any negative value – If all values are positive, eliminate the smallest value A B C AB + BC > AC; AC + BC > AB; AB + AC > BC