Complete the condition statements that must be met to order for three side lengths-a, b, and c- to create a triangle. a b+cand a b-c
The condition statements that must be met to order three side lengths, a, b, and c, to create a triangle are:
For a, b, and c to form a triangle:
1) The sum of any two side lengths should be greater than the third side length:
a + b > c
b + c > a
a + c > b
For a, b, and c to be the sides of a non-degenerate triangle (a triangle with positive area):
2) The difference between the lengths of any two sides should be less than the third side length:
|a - b| < c
|b - c| < a
|a - c| < b
So, the complete condition statements are:
a + b > c,
b + c > a,
a + c > b,
|a - b| < c,
|b - c| < a, and
|a - c| < b
If all of these conditions are satisfied, then the three side lengths, a, b, and c, can form a triangle.