To determine if a set of side measures can form a triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply the theorem to each set of side measures:
1) 2, 7, 6:
The sum of the first two sides (2 + 7) is 9, which is greater than the third side (6).
The sum of the second and third sides (7 + 6) is 13, which is greater than the first side (2).
The sum of the first and third sides (2 + 6) is 8, which is not greater than the second side (7).
Therefore, this set of side measures (2, 7, 6) can form a triangle.
2) 8, 1, 7:
The sum of the first two sides (8 + 1) is 9, which is not greater than the third side (7).
Therefore, this set of side measures (8, 1, 7) cannot form a triangle.
3) 12, 10, 22:
The sum of the first two sides (12 + 10) is 22, which is greater than the third side (22).
Therefore, this set of side measures (12, 10, 22) cannot form a triangle.
4) 9, 4, 3:
The sum of the first two sides (9 + 4) is 13, which is greater than the third side (3).
The sum of the second and third sides (4 + 3) is 7, which is not greater than the first side (9).
Therefore, this set of side measures (9, 4, 3) cannot form a triangle.
In conclusion, the group of side measures that can form a triangle is 2, 7, 6.
Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses 2, 7, 6 2, 7, 6 8, 1, 7 8, 1, 7 12, 10, 22 12, 10, 22 9, 4, 3
1 answer
1 answer