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5.5 Triangle Inequality. Objectives: Use the Triangle Inequality.

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Presentation on theme: "5.5 Triangle Inequality. Objectives: Use the Triangle Inequality."— Presentation transcript:

1 5.5 Triangle Inequality

2 Objectives: Use the Triangle Inequality

3 Triangle Inequality The sum of the lengths of any two sides of a Triangle is greater than the length of the third side. AB + BC > AC AC + BC > AB AB + AC > BC

4 Example: Solve for x: (x + 2) +(x + 3) > 3x – 2 2x + 5 > 3x – 2 5 > x – 2 7 > x

5 AB + BC > AC AC + BC > AB AB + AC > BC

6 AB + BC > AC AC + BC > AB AB + AC > BC

7 AB + BC > AC AC + BC > AB AB + AC > BC

8 AB + BC > AC AC + BC > AB AB + AC > BC

9 EXAMPLE Find possible side lengths ALGEBRA A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side. SOLUTION Let x represent the length of the third side. Steps: 1.Subtract two given numbers (That’s your smallest side) 2.Add two given numbers (That’s your longest side)

10 EXAMPLE Find possible side lengths Small values of x Large values of x x + 8 > 12 x >4 8 + 12> x x < 20 The length of the third side must be greater than 4 and less than 20. ANSWER

11 GUIDED PRACTICE for Example 3 3. A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side. 4 < x < 26 ANSWER EXAMPLE x + 11 > 15 x >4 11 + 15> x x < 26 Steps: 1.Subtract two given numbers (That’s your smallest side) 2.Add two given numbers (That’s your longest side)

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