complete the condition statement that must be met in order for three side lengths -a, b, and c- to create a triangle.

Question

a__b + c and a__b - c

the options are <, >, or =

Answer 1

a < b + c and a > b - c

Answer 2

explain why

Answer 3

In order for three side lengths a, b, and c to form a triangle, they must satisfy the triangle inequality theorem, which 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 side lengths to form a triangle, we should have:
a < b + c (sum of lengths of any two sides should be greater than the length of the third side)
a > b - c (difference between the lengths of any two sides should be less than the length of the third side)

If these conditions are not met, then it is impossible for the three side lengths to form a triangle.