Which Lengths make a Triangle? (1.2)

Author:
Roger Gemberling
As you explore the characteristics of triangles, one idea to explore is "Which lengths make a Triangle?" Use the GeoGebra sketch to answer the five multiple choice questions. Move the point on the slider to change the length of the third side. Move the green points (B and C) until you are able to place both points labeled C on top of each other. If both points labeled C are on top of each other, the three lengths make a triangle.

Question 1

You are asked to make a triangle with lengths of 5, 12, and 15. Is it possible? Two of the three lengths are already given. So move the point on the slider to 15, then try to complete the triangle by placing one point C exactly on top of the other point C.

Select all that apply
  • A
  • B
  • C
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Question 2

You are asked to make a triangle with lengths of 5, 12, and 8. Is it possible?

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  • A
  • B
  • C
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Question 3

You are asked to make a triangle with lengths of 5, 12, and 6. Is it possible?

Select all that apply
  • A
  • B
  • C
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Question 4

You are asked to make a triangle with lengths of 5, 12, and 11. Is it possible? .

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  • A
  • B
  • C
  • D
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Question 5

You are asked to make a triangle with lengths of 5, 12, and 18. Is it possible?

Select all that apply
  • A
  • B
  • C
Check my answer (3)
Now you will further explore which lengths make triangles. In the GeoGebra sketch, you are given 3 lengths. Place the three lengths in the spreadsheet in order from shortest to longest. Also enter the sum of sides 1 and 2 into your spreadsheet. Move the green points so they are exactly on top of each other. Then place either "Y" or "N" to indicate if a triangle is possible for the given lengths. Click on Next Problem to explore other combinations. Create a table with 12 examples. Make sure you have examples of both situations (work or don't work).

Question 6

For each set of lengths that make a triangle. how does the sum of side1 + side 2 compare to the length of side 3?

Complete this Conjecture

If you are given three lengths in order from shortest to longest, you will have a triangle when ...

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  • A
  • B
  • C
  • D
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