5'5: The Triangle Inequality

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5.5 The Triangle Inequality

• Do you think it is possible to rearrange these
  segments to form a triangle. (You must connect
  the points nothing can be overlapping.)

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• What about these three?

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• Works Doesnt Work
• Do you see a possible difference in the two?

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• Triangle Inequality Theorem The sum of the
  lengths of any two sides of a triangle must be
  greater than the third side.
• Ex. Determine if the sets of three measurements
  could form a triangle
• 1. 18, 45, 21 2. 18, 45, 52

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• Ex. You have three pieces of fence, 2 ft., 2.ft,
  and 4 ft. Can you make a triangular fence?
  Explain why or why not.

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• Ex. If two sides of a triangle measure 10 and 15
  cm. what are all the possible lengths the third
  side could be.
• Now assume that 10 and 15 are the two shortest
  sides
• What is the longest the third side could be and
  still work?

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• 2. Now assume 10 and 15 are the shortest sides
• What is the largest possible measurement I could
  have for the third side?

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• In other words, the third side must be larger
  than 5 cm, but smaller than 15 cm.
• An easy way to write this is 5 lt x lt 15, where x
  is the measure of the third side.
• So, two sides of 10 and 15, and we get
  measurements from 5 to 15. What is an easier way
  to come up with those numbers rather than going
  through those two steps?

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• Give all possible values for the third side of a
  triangle with the two given sides.
• 8 cm and 18 cm 2. 1 cm and 12 cm
• 3. 84 cm and 84 cm 4. 15 cm and 30 cm