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Apply inequalities in one triangle.

Learn how to apply inequalities in triangles, order side lengths and angles, understand Triangle Inequality Theorem, calculate possible side lengths, and solve travel distance scenarios in California. Check out various examples to enhance your understanding.

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Apply inequalities in one triangle.

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  1. Objectives Apply inequalities in one triangle.

  2. The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles.

  3. Example 1A: Ordering Triangle Side Lengths and Angle Measures Write the angles in order from smallest to largest.

  4. Example 1B: Ordering Triangle Side Lengths and Angle Measures Write the sides in order from shortest to longest.

  5. Check It Out! Example 2a Write the angles in order from smallest to largest.

  6. Check It Out! Example 2b Write the sides in order from shortest to longest.

  7. A triangle is formed by three segments, but not every set of three segments can form a triangle.

  8. A certain relationship must exist among the lengths of three segments in order for them to form a triangle.

  9. Example 3A: Applying the Triangle Inequality Theorem Tell whether a triangle can have sides with the given lengths. Explain. 7, 10, 19

  10. Example 3B: Applying the Triangle Inequality Theorem Tell whether a triangle can have sides with the given lengths. Explain. 2.3, 3.1, 4.6

  11. Example 4a: Finding Side Lengths The lengths of two sides of a triangle are 8 inches and 13 inches. Find the range of possible lengths for the third side.

  12. Check It Out! Example 4b The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side.

  13. Example 5a: Travel Application The figure shows the approximate distances between cities in California. What is the range of distances from San Francisco to Oakland?

  14. Check It Out! Example 5b The distance from San Marcos to Johnson City is 50 miles, and the distance from Seguin to San Marcos is 22 miles. What is the range of distances from Seguin to Johnson City?

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