Check if three side lengths can form a valid triangle using the triangle inequality theorem. Get detailed explanations and step-by-step verification.
Enter three side lengths and click "Check Triangle" to see if they can form a valid triangle.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This fundamental principle determines whether three given lengths can form a triangle.
a + b > c
Sum of first two sides > third side
a + c > b
Sum of first and third sides > second side
b + c > a
Sum of second and third sides > first side
Geometric Intuition: Imagine trying to connect three sticks end-to-end to form a triangle. If one stick is too long compared to the other two, they won't be able to meet and close the triangle.
Real-World Example: If you have sides of length 2, 3, and 10, you can't form a triangle because even when the 2 and 3 are stretched as far as possible (sum = 5), they can't reach the other end of the side with length 10.
Try other triangle calculators for different properties.