Triangle Inequality Theorem
Move the segments into a triangle. The points must meet at a vertex. The side lengths are 3, 4, and 5 units.
What do you notice about the triangle made from these segments?
Make a triangle using these segments. Be sure to match up the points. The segments are 2, 3, and 4 units long.
The 3 segments are 2 units, 5 units, and 8 units long. Move the segments to connect the points to make a triangle.
What do you notice about making a triangle with these three segments?
Make a triangle with side lengths of 10, 10, and 12.
What do you notice about these side lengths and making a triangle?
Will these segments make a triangle? Try it! The side lengths are 4, 6, and 11 units.
What do you notice about the side lengths and making a triangle with them? Why does this happen?
Triangle Inequality Theorem
It is not true that ANY three segments will make a triangle. Only line segments of certain lengths can form the three sides needed for a triangle.
The Triangle Inequality Theorem states the sum of any two sides of a triangle must be greater than the length of the third side.
Try It!
The triangle below is made up of segment AB, segment AC, and segment BC. The vertices of the triangle are moveable.
Move the vertices of the triangle to get the new lengths of the segments.
Informally prove the Triangle Inequality Theorem by adding two side lengths and comparing the sum to the third side.
For example, if the side lengths are
AB=5.89
AC=6.86
BC=6.81
then
AB + AC = 12.75, this is greater than BC
BC + AC = 13.67, this is greater than AB
AB + BC = 12.70, this is greater than AC