The Triangle Inequality

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Triangle Inequalities

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Presentation transcript:

The Triangle Inequality

Theorem 5.11 Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B Example: AB + BC > AC BC + AC > AB AB + AC > BC C A

Determine whether the given measures can be the sides of a triangle. NO! 6 ½ + 6 ½ > 14 ½ 13 > 14 ½ is false. 6.8 + 7.2 > 7.5 14 > 7.5 B) 6.8, 7.2, 7.5 6.8 + 7.5 > 7.2 14.3 > 7.2 YES! 7.2 + 7.5 > 6.8 14.7 > 6.8 Hint: Take the two smallest numbers and add them together. They have to be larger than the third number or the side lengths cannot form a triangle.

Practice Can these numbers form the sides of a triangle? 3, 7, 9 3 + 7 = 10 , 10 > 9, YES! 2, 3, 6 2 + 3 = 5, 5 IS NOT GREATER THAN 6, NO! 10, 10, 19 10 + 10 = 20, 20 > 19, YES!

Given the measures of two sides determine the range of the third Given:  ABC with AB = 7 and BC = 12, determine the range of AC. Solve AB + BC > AC BC + AC > AB AB + AC > BC B AB + BC > AC 7 + 12 > AC 19 > AC BC + AC > AB 12 + AC > 7 AC > -5 AB + AC > BC 7 + AC > 12 AC > 5 A C Thus AC is less than 19 and greater than 5! Hint: Add the two numbers together and then subtract the two numbers! Those are your range values!