Enter the lengths of any two sides of the triangle into the calculator to determine if the sum of these two sides is greater than the length of the third side, as this inequality must be satisfied for the triangle to be valid according to the Triangle Inequality Theorem.
Triangle Inequality Theorem Formula
The following formula is used to calculate the Triangle Inequality Theorem:
a + b > c
Variables:
- a, b, and c are the lengths of the sides of the triangle
To determine if a triangle is valid, add the lengths of any two sides of the triangle. The sum of these two sides must be greater than the length of the third side. If this inequality is satisfied, then the triangle is valid. Otherwise, it is not a valid triangle according to the Triangle Inequality Theorem.
What is a Triangle Inequality Theorem?
The Triangle Inequality Theorem is a fundamental principle in geometry that states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is a direct consequence of the Euclidean geometry postulate that the shortest distance between two points is a straight line. It is used to determine if a triangle can be formed given three line segments. If the sum of the lengths of the two shorter segments is greater than the length of the longest segment, then a triangle can be formed. Conversely, if the sum of the lengths of the two shorter segments is less than or equal to the length of the longest segment, then a triangle cannot be formed. This theorem is not only applicable in geometry but also in other fields such as physics and computer science.
How to Calculate Triangle Inequality Theorem?
The following steps outline how to apply the Triangle Inequality Theorem.
- First, gather the lengths of the three sides of the triangle.
- Next, compare the sum of the lengths of any two sides to the length of the remaining side.
- If the sum of the lengths of any two sides is greater than the length of the remaining side, then the triangle is valid.
- If the sum of the lengths of any two sides is equal to the length of the remaining side, then the triangle is degenerate (a straight line).
- If the sum of the lengths of any two sides is less than the length of the remaining side, then the triangle is invalid.
Example Problem:
Use the following lengths as an example problem to test your knowledge.
Side A: 5 units
Side B: 7 units
Side C: 10 units
