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Triangle Inequality TheoremRule explainedTriangle Formulas | Triangles | Triangle Types | Interactive Triangle | Remote Interior Angles | Area of a Triangle | Triangle Inequality Theorem images 
Free Triangle Worksheets
The TheoremThe Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the the measure of the third side. Otherwise, you cannot create a triangle from the 3 sides. This rule must be satisfied for all 3 permutations of the sides. In other words, as soon as you know that the sum of 2 sides is less than the measure of a third side, then you know that the sides do not make up a triangle . 
Demonstrations illustrating the Triangle Inequality Theorem
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!
Demonstration 1: When the sum of 1 pair of sides exactly equals the measure of a 3rd side.
Demonstration 2 When the sum of 1 pair of sides is less than the measure of a 3rd side.
Practice Problems involving the Triangle Inequality Theorem
Could a triangle have side lengths of
Side 1: 4 Side 2: 8 Side 3: 2
Use the triangle inequality theorem and examine all 3 combinations of the sides. As soon as the sum of any 2 sides is less than the third side then the triangle's sides do not satisfy the theorem.
Could a triangle have side lengths of
Side 1: 5 Side 2: 6 Side 3: 7
Use the triangle inequality theorem and examine all 3 combinations of the sides. In this case, all of the pairings of sides satisfy this theorem
Could a triangle have side lengths of
Side 1: 6 Side 2: 8 Side 3: 15
Use the triangle inequality theorem and examine all 3 combinations of the sides. In this case, the first pair that I checked did not have a sum greater than the third. One of the nice qualities of the inequality theorem is that as soon as you find 1 pair of sides that is not greater than the the third, you do not need to look any further -- you already know that the three sides cannot form a triangle .
Do the side lengths below satisfy the triangle inequality theorem
Side 1: 7 Side 2: 9 Side 3: 15
Use the triangle inequality theorem and examine all 3 combinations of the sides.
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Graphing Calc
