Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle. (1 point)
A. 8, 8, 20
B. 20, 10, 30
C. 8, 4, 12
D. 10, 20, 15
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.
Based on this theorem, we can determine which three side lengths form a triangle:
A. 8, 8, 20: Since 8 + 8 = 16 is less than 20, this does not form a triangle.
B. 20, 10, 30: Since 20 + 10 = 30, this does not form a triangle.
C. 8, 4, 12: Since 8 + 4 = 12, this does not form a triangle.
D. 10, 20, 15: Since 10 + 15 = 25 is greater than 20, 10 + 20 = 30 is greater than 15, and 20 + 15 = 35 is greater than 10, this forms a triangle.
Therefore, the three side lengths that form a triangle are 10, 20, and 15.