Triangle inequality theorem

The  exercise appears under the Geometry Math Mission. This exercise introduces the Triangle Inequality Theorem.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine if the triangle is possible: This problem has a triangle with its three sides labeled. The student is asked to determine if a triangle with those labeled sides can even exist.Tithe1.png
 * 2) Find range of possible side lengths: This problem provides a triangle with two given sides. The student is asked to find the range of possibilities for the third side of the triangle.Tithe2.png

Strategies
Knowledge of the Triangle Inequality is encouraged to ensure success on this exercise.
 * 1) The version of the Triangle Inequality used in this exercise is summarized as "The sum of the lengths of two sides of a triangle exceeds the length of the third side."
 * 2) Another characterization is useful for the Find the range of possible side lengths problem. The third side of a triangle lies strictly between the difference and the sum of the other two sides.
 * 3) Another version of the Triangle Inequality is sometimes referred to as the "Hinge Theorem." It states that in a triangle the largest angle is opposite from the largest side.

Real-life Applications

 * 1) The Triangle Inequality is useful for finding possible ranges of lengths on maps.
 * 2) Applications of the Triangle Inequality are a common problem on many standardized tests such as the SAT.
 * 3) Since real-life is not exact, bounds on size (especially good bounds) are often more useful than exact answers. This exercise practices one of the earliest "bounding" theorems.