Chapter 5 Section 5.5

1. Chapter 5Section 5.5 Inequalities in a triangle

2. -3 -3 +9 -2x -10 -10 +9 -2x -1 2 -1 2 Don’t forget to change it! 3 < 2x - 9 x < 11 2 > -x 12 < 2x -2<x 6<x

3. Compare Sides to Order Angles C B A Theorem 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. mA > mB > mC CB > CA > AB

4. Compare Angles to Order Sides R P Q Theorem 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. mP > mQ > mR QR > PR > PQ

5. mM > mK > mL KL > LM > KM

6. mM > mO > mN ON > MN > OM

7. mB > mA > mC AC > BC> AB

8. EG > GF > EF mF > mE > mG

9. mJ > mI > mH HI > HJ > IJ

10. LM > KM > KL mK > mL > mM

11. In ABC CB > AB > AC In CBD BD > CD > CB Thus BD > CD > CB > AB > AC

12. In LKM LM > KL > KM In LMN MN > LN > LM Thus MN > LN > LM > LN > LM

13. Inequalities in a triangle R P Q T Theorem Theorem 5.12 Exterior Angle Inequality The measure of an exterior angle of a triangle is greater than the measure of the two nonadjacent interior angles. TQR is an exterior angle of QRP mTQR > mR And mTQR > mP

14. Inequalities in a triangle Theorem Theorem 5.13 Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC AB + AC > BC BC + AC > AB

16. The sum of any two sides must be greater than the third side! YZ + XY > XZ XZ + XY > YZ XZ + YZ > XY 2 + XY > 3 3 + XY > 2 2 + 3 > XY XY > 1 5 > XY XY > -1 5 > XY > 1

17. The sum of any two sides must be greater than the third side! YZ + XY > XZ XZ + XY > YZ XZ + YZ > XY 8 + XY > 10 10 + XY > 8 8 + 10 > XY XY > 2 18 > XY XY > -2 18 > XY > 2

18. CC 60 AF 40 DS 60 + x > 40 60 + 40 > x x + 40 > 60 100 > x x > -20 x > 20 x 100 > x > 20 No, the distance must be less than 100 miles

19. HW #59Pg