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Apply inequalities in one triangle.

Objectives. Apply inequalities in one triangle. The positions of the longest and shortest sides of a triangle are related to the positions of the largest and smallest angles. Example 1a. Write the angles in order from smallest to largest. Example 1b.

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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 Write the angles in order from smallest to largest.

  4. Example 1b Write the sides in order from shortest to longest.

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

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

  7. Example 2a Tell whether a triangle can have sides with the given lengths. Explain. 8, 13, 21

  8. Example 2b Tell whether a triangle can have sides with the given lengths. Explain. 6.2, 7, 9

  9. Example 2c Tell whether a triangle can have sides with the given lengths. Explain. t – 2, 4t, t2 + 1, when t = 4

  10. Example 3 The lengths of two sides of a triangle are 22 inches and 17 inches. Find the range of possible lengths for the third side.

  11. Example 4: Travel Application The figure shows the approximate distances between cities in California. What is the range of distances from San Francisco to Oakland?

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