Apply the Triangle Inequality Theorem to determine which three side lengths form a 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.
For example, let's say we have three side lengths:
- Side 1: 5 units
- Side 2: 7 units
- Side 3: 10 units
We can apply the Triangle Inequality Theorem to determine if these three side lengths can form a triangle:
- Side 1 (5 units) + Side 2 (7 units) = 12 units, which is greater than Side 3 (10 units)
- Side 1 (5 units) + Side 3 (10 units) = 15 units, which is greater than Side 2 (7 units)
- Side 2 (7 units) + Side 3 (10 units) = 17 units, which is greater than Side 1 (5 units)
Since all three combinations of two sides satisfy the Triangle Inequality Theorem, these three side lengths can form a triangle.