1. Inequalities in One Triangle SECTION 6.5

2. Exploration: Triangle Inequalities: Do this on your white paper… 1.Draw an obtuse scalene triangle with your pencil. 2.Measure the angles using a protractor and sides using ruler. 3.Find the largest angle and the longest side and mark them in red. Find the smallest angle and the shortest side and mark them in blue. 4. Compare with your neighbor. Write down one thing that you notice on your paper.

3. Student Journal Page 186

4. Student Journal Page 187

5. 1.a) Is it possible to construct a triangle with sides 5, 6, 7? b) Is it possible to construct a triangle with sides 12, 17, 5? Student Journal Page 187 2. A triangle has one side of length 6 and another side of length 15. Describe the possible lengths of the third side. USE THE TRIANGLE INQEQUALITY THEOREM: The sum of the two shortest lengths must be more than the longer side. USE THE TRIANGLE INQEQUALITY THEOREM: The sum of the two shortest lengths must be more than the longer side. BUT we don’t know which sides are the smallest or the largest, so we must test all scenarios.

6. Student Journal Page 188 Since AB<BC<AC then From smallest to largest the angles are: <C, <A, <B. Since EF<DF<ED then From smallest to largest the angles are: <D, <E, <F. Since GJ<GH<HJ then From smallest to largest the angles are: <H, <J, <G. USE THE TRIANGLE LONGER SIDE THEOREM

7. Student Journal Page 188 3 and 12 are the shortest lengths: 3+12=15 Since 15 is NOT more than 17, then; IS NOT possible to construct a triangle with side lengths 3, 12, 17. USE THE TRIANGLE INQEQUALITY THEOREM: The sum of the two shortest lengths must be more than the longer side. 5 and 16 are the shortest lengths: 5+16=21 Since 21 is NOT more than 21, then; IT IS NOT possible to construct a triangle with side lengths 5, 21, 16. 5 and 7 are the shortest lengths: 5+7=12 Since 12 is more than 8, then; IT IS possible to construct a triangle with side lengths 8, 5, 7. 10 and 3 are the shortest lengths: 10+3=13 Since 13 is more than 11, then; IT IS possible to construct a triangle with side lengths 10, 3, 11.

8. Student Journal Page 188 x + 5 > 13 ; 5 + 13 > x Or subtract 5 and 13 and then add 5 and 13 The possible lengths of the third side of the triangle are: 8 < x < 18 The third side can be: 9, 10, 11, 12, 13, 14, 15, 16, 17 The third side CANNOT BE 8 or less. The third side CANNOT BE 18 or more. USE THE TRIANGLE INQEQUALITY THEOREM: The sum of the two shortest lengths must be more than the longer side. BUT we don’t know which sides are the smallest or the largest, so we must test all scenarios.

9. THE END