Complete the condition statements that must be met in order for three side lengths— a , b , and c —to create a triangle.(1 point)
a
b+c and a
b−c
In order for three side lengths a, b, and c to create a triangle, the following conditions must be met:
1) Triangle Inequality Theorem: The sum of any two side lengths of a triangle must be greater than the third side length. Therefore, for side lengths a, b, and c:
a + b > c
a + c > b
b + c > a
2) Non-negative difference: The difference between two side lengths must be non-negative. Therefore, for side lengths a, b, and c:
a - b ≥ 0
a - c ≥ 0
b - c ≥ 0
These conditions ensure that the side lengths can form a closed shape with three sides, which is the definition of a triangle.