Triangle Inequality
The above animation displays how if given a line segment of three inches, that a triangle is not formed until HG + IE are greater than three inches. Notice that when HG + IE equal three inches, they form the line segment HI. This special case is called a degenerate triangle, or in other words no triangle.
Using Geometer's Sketchpad (or ruler and compass) can you construct the following triangles?
| # 1. 6 cm, 5 cm, 4 cm | # 2. 6 cm,6 cm, 4 cm | # 3. 5 cm, 5 cm, 5 cm |
| # 4. 3 cm, 3.5 cm, 6.5 cm | # 5. 3.5 cm, 2.5 cm, 6.5 cm | # 6. 5 cm, 3 cm, 2 cm |
#7. Which of the above did not result in a triangle? What is true about the sum of the lengths of the shorter sides?
#8. Which of the above did result in a triangle? What is true
about the sum of the lengths of the shorter sides? Name each type of triangle
formed.
#9. List three sets of three lengths that can be used to construct
a triangle. Do not use more than one set in which all the lengths are equal.
#10. List three sets of three lengths that can not be used to construct
a triangle.
#11. What can you conclude about the lengths of the sides of a triangle?