Apply the triangle inequality theorem to determine which three sides form a triangle
To apply the triangle inequality theorem, we have to compare the sum of the lengths of any two sides of a triangle with the length of the third side.
Let's say we have three sides with lengths a, b, and c.
According to the triangle inequality theorem, for a triangle to be formed:
- The sum of the lengths of any two sides must be greater than the length of the third side.
So, for the sides a, b, and c to form a triangle, we must have:
- a + b > c
- a + c > b
- b + c > a
If all three conditions are met, then the sides a, b, and c can form a triangle. If any of the conditions are not met, then those sides cannot form a triangle.