According to Triangle Inequality, there are certain
sets of measurements that cannot be used to form triangles. For example, it is
impossible to form a triangle with sides measuring 2, 3, and 6 units, because 2 + 3 <
6.
The animation below displays how if given a line segment of
three inches, 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.
If you know the measures of two sides of a triangle, can you
use the Triangle Inequality to determine the greatest and least possible measure
of the third side of the triangle?
