what are the condition statements that must be met in order for three side lengths— a , b , and c —to create a triangle? :)
The condition statements that must be met in order for three side lengths, a, b, and c, to create a triangle are:
1. The sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
(a + b > c)
(b + c > a)
(c + a > b)
2. The difference between the lengths of any two sides of the triangle must be smaller than the length of the third side.
(|a - b| < c)
(|b - c| < a)
(|c - a| < b)
3. All three side lengths must be greater than zero.
(a > 0)
(b > 0)
(c > 0)
If all these conditions are met, then the three side lengths can form a triangle.
so for : a ___ b + c and a ____ b - c
For the condition a > b + c to be met, it means that side a must be larger than the sum of sides b and c. This condition ensures that no side of a triangle can be longer than the combined lengths of the other two sides.
For the condition a > b - c to be met, it means that side a must be larger than the difference between sides b and c. This condition ensures that no side of a triangle can be shorter than the difference between the other two sides.
If either of these conditions is not met, it would mean that the given side lengths cannot form a triangle.