For instance, can I create a triangle from sides of length...say 4, 8 and 3?
No!It's actually not possible!
As you can see in the picture below, it's not possible to create a triangle that has side lengths of
4, 8, and 3
It turns out that there are some rules about the
side lengths of triangles.
You can't just make up 3 random numbers and have a
triangle! You could end up with 3 lines like those pictured above that
cannot be connected to form a triangle.
Video On Theorem
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the
measure of the third side.
Note: This rule must be satisfied for all 3 conditions of the sides.
In other words, as soon as you know that the sum of 2 sides is less than (or equal to) the measure of a third side,
then you know that the sides do not make up a
The interactive demonstration below shows that the sum of the lengths of any 2 sides of a triangle must
exceed the length of the third side. The demonstration also illustrates what happens when the sum of 1 pair of sides
equals the length of the third side--you end up with a straight line! You can't make a triangle!
Otherwise, you cannot create a triangle
from the 3 sides.
When the sum of 1 pair of sides exactly equals the measure of a 3rd side.
When the sum of 1 pair of sides is less than the measure of a 3rd side.