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Section 5-5 Inequalities in triangles

Learn about comparison properties and theorems involving inequalities in triangles, including Theorem 5-10 and Theorem 5-11. Explore examples to understand how to apply these concepts in triangle geometry.

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Section 5-5 Inequalities in triangles

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  1. Section 5-5 Inequalities in triangles GEOMETRY

  2. Comparison Property of Inequality If and , then . Given: Prove:

  3. Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

  4. Example 1: You are building a deck and want to put benches in the two largest corners, but which corners are the largest?

  5. Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

  6. Example 2: Which side is shortest?

  7. Theorem 5-12 (Triangle Inequality Thm):The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

  8. Example 3:

  9. Example 4: The lengths of two sides of a triangle are given. Describe the lengths possible for the third side. A. B.

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