Complete the condition statements that must be met in order for three side lengths—a, b, and c—to create a triangle.
a b+c and a b−c
Well, to create a triangle, we need two conditions to be satisfied:
1) The sum of any two side lengths must be greater than the third side length. So, for a triangle with side lengths a, b, and c, the condition would be a < b + c.
2) The difference between any two side lengths must be less than the third side length. So, for a triangle with side lengths a, b, and c, the condition would be a > |b - c|.
Now, combined, the conditions for a, b, and c to create a triangle would be:
a < b + c and a > |b - c|.
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 any two sides must be greater than the third side. This can be written as a + b > c, a + c > b, and b + c > a.
2. The difference between any two sides must be less than the third side. This can be written as a - b < c, a - c < b, and b - c < a.
Therefore, the correct condition statements are:
a + b > c and a + c > b and b + c > a
and
a - b < c and a - c < b and b - c < a
In order for three side lengths a, b, and c to create a triangle, the following conditions must be met:
1. Triangle Inequality Theorem:
- Side a must be greater than the difference between sides b and c (a > |b - c|).
- Side a must be less than the sum of sides b and c (a < b + c).
Combining these conditions, the complete condition statements are:
1. a > |b - c|
2. a < b + c
To determine the condition statements that must be met in order for three side lengths (a, b, and c) to create a triangle, we need to consider the Triangle Inequality Theorem.
According to the Triangle Inequality Theorem, for any triangle:
1) The sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
2) The difference between the lengths of any two sides of the triangle must be less than the length of the third side.
Based on the given side lengths a, b, and c, we can write the two condition statements:
1) a + b > c
The sum of side lengths a and b must be greater than the length of side c.
2) a - b < c
The difference between side lengths a and b must be less than the length of side c.
These two condition statements ensure that the three side lengths (a, b, and c) satisfy the Triangle Inequality Theorem and can indeed form a valid triangle.