Question

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

Answer 1

fill in the blanks a__ b+c and a __ b-c

Answer 2

To determine if three side lengths \( a \), \( b \), and \( c \) can form a triangle, they must satisfy the triangle inequality conditions. These conditions can be stated as follows:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

For the specific statements you're trying to complete, they would be:

1. \( a + b > c \) (This means that the sum of sides \( a \) and \( b \) must be greater than side \( c \)).
2. \( a + c > b \) (This means that the sum of sides \( a \) and \( c \) must be greater than side \( b \)).

So, completing the provided statements:

- \( a + b > c \)
- \( a + c > b \)

If you need to fill in blanks:
- \( a > b - c \) (which comes from rearranging the second inequality)
- \( a < b + c \) (which comes from rearranging the first inequality)

Please clarify if there's any specific format you're looking for!