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Triangle Inequality Theorems and Corollaries

Learn about triangle inequalities, including relationships between sides and angles, the triangle inequality theorem, and the SAS and SSS Inequality Theorems. Discover how to determine the largest and smallest angles and sides in a triangle.

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Triangle Inequality Theorems and Corollaries

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  1. Inequalities in Triangles Section 6-4, 6-5

  2. Inequalities for one triangle theorems. • If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

  3. Which is the largest and smallest angle.

  4. Inequalities for one triangle theorems cont. • If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

  5. Which is the largest and smallest side?

  6. Inequalities for one triangle corollaries • The perpendicular segment from a point to a line is the shortest segment from the point to the line. • The perpendicular segment from a point to a plane is the shortest segment from a point to the plane.

  7. The triangle inequality • The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  8. Which set(s) of side lengths will not make a triangle • 3, 4, 5 • 1, 4, 6 • 8, 2, 6 • 5, 5, 5 • 10, 13, 2

  9. What is the largest and smallest length possible for the third side?

  10. SAS Inequality Theorem • If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second

  11. SAS InequalityTheorem

  12. SSS Inequality Theorem • If two sides of one triangle are congruent to two sides of another triangle, and third side of the first is longer than the third side of the second, then the included of the first is larger than the included angle of the second

  13. SSS InequalityTheorem

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