apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle.(1 point) Responses
9, 4, 3
9, 4, 3
12, 10, 22
8, 1, 7
2, 7, 6
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.
Using this theorem, we can determine which group of side measures will form a triangle:
- For the group of side measures 9, 4, 3:
9 + 4 > 3 (True)
9 + 3 > 4 (True)
4 + 3 > 9 (False)
Since one of the sums is not greater than the third side, this group of side measures (9, 4, 3) will not form a triangle.
- For the group of side measures 12, 10, 22:
12 + 10 > 22 (False)
12 + 22 > 10 (True)
10 + 22 > 12 (True)
Since all the sums are greater than the third side, this group of side measures (12, 10, 22) will form a triangle.
- For the group of side measures 8, 1, 7:
8 + 1 > 7 (True)
8 + 7 > 1 (True)
1 + 7 > 8 (True)
Since all the sums are greater than the third side, this group of side measures (8, 1, 7) will form a triangle.
- For the group of side measures 2, 7, 6:
2 + 7 > 6 (True)
2 + 6 > 7 (True)
7 + 6 > 2 (True)
Since all the sums are greater than the third side, this group of side measures (2, 7, 6) will form a triangle.