The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
To determine which group of side measures will form a triangle, we need to check if the triangle inequality holds true for the given side measures.
Let's consider three side measures: a, b, and c.
If a + b > c, a + c > b, and b + c > a, then we can form a triangle using these side measures.
For example, if the side measures are 3, 4, and 5, we can check if the triangle inequality holds true:
3 + 4 > 5
4 + 5 > 3
5 + 3 > 4
Since all three inequalities are true, these side measures (3, 4, and 5) will form a triangle.
However, if we have side measures like 1, 2, and 6, we can check if the triangle inequality holds true:
1 + 2 > 6
2 + 6 > 1
6 + 1 > 2
In this case, the first inequality (1 + 2 > 6) is false. Thus, these side measures (1, 2, and 6) will not form a triangle.
Therefore, to determine which group of side measures will form a triangle, we need to check if all three inequalities of the triangle inequality theorem are true for the given side measures.
Apply the triangle inequality theorem and determine which group of side measures will form a triangle
1 answer