Which Lengths make a Triangle? (1.1)

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.

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
Check my answer (3)

Question 2

You are asked to make a triangle with lengths of 5, 12, and 8. Is it possible? Two of the three lengths are already given. So move the point on the slider to 8, 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
Check my answer (3)

Question 3

You are asked to make a triangle with lengths of 5, 12, and 6. Is it possible? Two of the three lengths are already given. So move the point on the slider to 6, 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
Check my answer (3)

Question 4

You are asked to make a triangle with lengths of 5, 12, and 11. Is it possible? Two of the three lengths are already given. So move the point on the slider to 11, 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
  • D
Check my answer (3)

Question 5

You are asked to make a triangle with lengths of 5, 12, and 18. Is it possible? Two of the three lengths are already given. So move the point on the slider to 18, 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
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. Move the green points so one green point is exactly on top on the 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.
Complete the Desmos activity as an exit ticket for this investigation. Make sure you sign in.

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