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

To determine if three side lengths \( a \), \( b \), and \( c \) can create a triangle, the following conditions must be met based on the triangle inequality theorem:

1. \( a < b + c \) (The length of one side must be less than the sum of the other two sides)
2. \( b < a + c \) (The length of one side must be less than the sum of the other two sides)
3. \( c < a + b \) (The length of one side must be less than the sum of the other two sides)

These conditions ensure that the three lengths can form a valid triangle.