Complete the condition statements that must be met in order for three side lengths— a , b , and c —to create a triangle.(1 point)

Question

a ___ b+c and a ___ b-c

Answer 1

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

1. \( a < b + c \) (the length of one side must be less than the sum of the lengths of the other two sides)
2. \( a > |b - c| \) (the length of one side must be greater than the difference of the lengths of the other two sides)

Thus, you can complete your statements as:

• \( a < b + c \)
• \( a > b - c \) (or equivalently \( a > |b - c| \) to cover the absolute value)

So, the full conditions are:

1. \( a < b + c \)
2. \( a > |b - c| \) (which encompasses both \( a > b - c \) and \( a > c - b \)).