To check the Triangle Inequality Theorem:
\[ a + b > c \]
And:
\[ a + c > b \]
And:
\[ b + c > a \]
Where:
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.
Let's assume the following values:
Using the theorem:
Since all conditions are satisfied, the sides form a valid triangle.
