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

1. \( a < b + c \)
2. \( a > |b - c| \)

So, the completed statements are:

• \( a < b + c \)
• \( a > b - c \) (this can also be expressed as \( a > |b - c| \))

Generally, the three conditions can be summarized as:

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

These inequalities ensure that the lengths can indeed form a triangle.