Complete the condition statements that be met in order for three side lengths a,b, and c to create a triangle

Answer 1

The condition statements that must be met in order for three side lengths a, b, and c to create a triangle are as follows:

1. Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- a + b > c
- b + c > a
- c + a > b

2. None of the side lengths can be negative: a, b, and c must all be positive real numbers.

3. The sum of any two side lengths must be greater than zero: a + b > 0, b + c > 0, and c + a > 0.

These conditions ensure that a, b, and c can form a closed, two-dimensional figure known as a triangle.