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

Question

a__b+c and a__b−c

Answer 1

To determine whether three side lengths \( a \), \( b \), and \( c \) can form a triangle, the following triangle inequalities must be satisfied:

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

So, for your statements, it would be:

• \( a < b + c \)
• \( a > b - c \)

However, the second part should actually be phrased to reflect the triangle inequality rule:

• \( a + b > c \)

In summary, the correct inequalities derived from the triangle inequality are:

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