Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
8, 4, 12
8, 8, 20
20, 10, 30
10, 20, 1
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.
1) For the first set of side lengths (8, 4, 12):
8 + 4 > 12 (true)
8 + 12 > 4 (true)
4 + 12 > 8 (true)
Therefore, the side lengths 8, 4, and 12 form a triangle.
2) For the second set of side lengths (8, 8, 20):
8 + 8 > 20 (false)
8 + 20 > 8 (true)
8 + 20 > 8 (true)
Therefore, the side lengths 8, 8, and 20 do not form a triangle.
3) For the third set of side lengths (20, 10, 30):
20 + 10 > 30 (false)
20 + 30 > 10 (true)
10 + 30 > 20 (true)
Therefore, the side lengths 20, 10, and 30 do not form a triangle.
4) For the fourth set of side lengths (10, 20, 1):
10 + 20 > 1 (true)
10 + 1 > 20 (false)
20 + 1 > 10 (true)
Therefore, the side lengths 10, 20, and 1 do not form a triangle.
So, only the side lengths 8, 4, and 12 form a triangle.