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5.5: Inequalities in Triangles

5.5: Inequalities in Triangles. Objectives: To use inequalities involving angles of triangles and to use inequalities involving sides of triangles. Comparison Property of Inequality. If a = b + c and c ≠ 0 , then a > b Apply this to the Triangle Exterior Angle Theorem: Therefore:.

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5.5: Inequalities in Triangles

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  1. 5.5: Inequalities in Triangles Objectives: To use inequalities involving angles of triangles and to use inequalities involving sides of triangles

  2. Comparison Property of Inequality If a = b + c and c ≠ 0, then a > b Apply this to the Triangle Exterior Angle Theorem: Therefore: 2 3 1

  3. Why is 3 1 4 2

  4. Theorem If 2 sides of a triangle are not congruent, then the larger angle lies opposite the longer side Y If XZ > XY, then X Z

  5. Theorem If 2 angles of a triangle are not congruent, then the longer side lies opposite the larger angle B If , then BC > AC C A

  6. Examples 1. List the angles in order from smallest to largest. 2. List the angles in order from largest to smallest in ∆ABC with AB = 15, BC=20, and AC = 30. J 6 G 8 7 C

  7. Examples 1. List the sides in order from longest to shortest. A 40 S 55 85 C

  8. List the sides in order from shortest to longest in ∆TFK with

  9. Triangle Inequality Theorem The sum of lengths of any 2 sides of a ∆ is greater than the length of the 3rd side. B AB + BC > AC AC + BC > AB AB + AC > BC C A

  10. Example • A triangle has sides of lengths 8 cm and 10 cm. Describe the possible lengths of the third side. The possible lengths will be greater than the difference and less than the sum of the 2 given sides

  11. Can a triangle have sides with the given lengths? Explain. • 6 ft, 8 ft, 2ft • 10 in, 15 in, 20 in • 12cm, 6cm, 4 cm

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