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

2 answers

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!

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