5.5 Triangle Inequality. Objectives: Use the Triangle Inequality.

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Presentation transcript:

5.5 Triangle Inequality

Objectives: Use the Triangle Inequality

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

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

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

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

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

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

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)

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

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 > > x x < 26 Steps: 1.Subtract two given numbers (That’s your smallest side) 2.Add two given numbers (That’s your longest side)