Question

Apply the triangle inequality theorem and determine which group of side measures will form a triangle

Answer 1

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.