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. [br][br]The Triangle Inequality Theorem states the sum of any two sides of a triangle must be greater than the length of the third side. [br][br][br]
Try It!
The triangle below is made up of segment AB, segment AC, and segment BC. The vertices of the triangle are moveable. [br][br][b][i]Move the vertices of the triangle to get the new lengths of the segments. [/i][/b][br][br]Informally prove the Triangle Inequality Theorem by adding two side lengths and comparing the sum to the third side. [br][br]For example, if the side lengths are[br]   AB=5.89[br]   AC=6.86[br]   BC=6.81[br][br]   then [br]   AB + AC = 12.75, this is greater than BC [br]   BC + AC = 13.67, this is greater than AB[br]   AB + BC = 12.70, this is greater than AC
Move the points to change the side lengths.
Close
– Tonia Hawf

Information: Triangle Inequality Theorem