Triangle Inequalities

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Triangle Inequalities
2
Definitions

• Theorem 5-12 Triangle inequality
• Theorem- Sum of the lengths of any two sides of a
  triangle is greater than the length of the third
  side.

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Example

• If the lengths of two sides of a triangle are ten
  centimeters and fifteen centimeters, between what
  two numbers must the measure of the third side
  fall?
• let t the length of the third side of the
  triangle
• By the Triangle Inequality Theorem, each of
  these inequalities must be true
• 1015 gtt 15tgt10 10tgt15
  (see example
• 25gtt tgt-5
  tgt5 2 page 268)
• The lengths of the third side must fall in the
  range included in all three inequalities