Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
8, 4, 12
20, 10, 30
10, 20, 15
8, 8, 20
According to the Triangle Inequality Theorem, for a triangle to be formed, 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 sets of side lengths form a triangle.
In the first set of side lengths, where the lengths are 8, 4, and 12, we can see that 8 + 4 = 12. However, 12 is not greater than the third side length of 12. Therefore, this set of side lengths does not form a triangle.
In the second set of side lengths, where the lengths are 20, 10, and 30, we can see that 20 + 10 = 30. However, 30 is not greater than the third side length of 30. Therefore, this set of side lengths does not form a triangle.
In the third set of side lengths, where the lengths are 10, 20, and 15, we can see that 10 + 15 = 25, which is greater than the third side length of 20. Additionally, 10 + 20 = 30, which is greater than the third side length of 15. Therefore, this set of side lengths does form a triangle.
In the fourth set of side lengths, where the lengths are 8, 8, and 20, we can see that 8 + 8 = 16, which is less than the third side length of 20. Therefore, this set of side lengths does not form a triangle.
So, out of the given sets of side lengths, only the set 10, 20, and 15 forms a triangle.