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 form a triangle, they must satisfy the triangle inequality theorem, which comprises three conditions:

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

From your statement, it seems you’re focusing on specific conditions related to \( a \). Here they are completed:

1. \( a < b + c \)
2. \( a > |b - c| \) (this corresponds to the condition \( a > b - c \) when \( b \) is greater than \( c \), and it also provides the lower bound for \( a \) based on triangles).

So, the complete conditions are:
- \( a < b + c \)
- \( a > |b - c| \)

This ensures that the lengths \( a \), \( b \), and \( c \) can form a triangle.