Apply the Triangle Inequality Theorem to determine which side lengths will form a triangle.
A. 1,2,3
B. 8,3,12
C. 10,9,1
D. 8,10,3
To determine which side lengths will form a triangle, we need to see if the sum of the lengths of any two sides is greater than the length of the third side.
A. 1, 2, 3: 1 + 2 > 3, 1 + 3 > 2, 2 + 3 > 1
These lengths can form a triangle.
B. 8, 3, 12: 8 + 3 > 12, 8 + 12 > 3, 3 + 12 > 8
These lengths can form a triangle.
C. 10, 9, 1: 10 + 9 > 1, 10 + 1 > 9, 9 + 1 > 10
These lengths can form a triangle.
D. 8, 10, 3: 8 + 10 > 3, 8 + 3 < 10
These lengths cannot form a triangle since the sum of the lengths of the two shorter sides is not greater than the length of the longest side.
Therefore, choices A, B, and C will form a triangle, but choice D will not.