Apply the Triangle Inequality Theorem and determine which group of side measures will form a triangle. (1 point)
A. 9,4. 3
B. 8, 1.7
C. 2,7.6
D. 12. 10, 22
To determine which group of side measures will 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 check each group of side measures:
A. 9, 4, 3
9 + 4 = 13
13 > 3
9 + 3 = 12
12 > 4
4 + 3 = 7
7 > 9
The lengths 9, 4, and 3 can form a triangle.
B. 8, 1.7
8 + 1.7 = 9.7
9.7 > None of the sides (1.7)
The lengths 8 and 1.7 cannot form a triangle.
C. 2, 7.6
2 + 7.6 = 9.6
9.6 > None of the sides (2)
The lengths 2 and 7.6 cannot form a triangle.
D. 12, 10, 22
12 + 10 = 22
22 > 12
10 + 12 = 22
22 > 10
12 + 22 = 34
34 > 10
The lengths 12, 10, and 22 can form a triangle.
Therefore, the groups of side measures that can form a triangle are A and D.