Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
8,8, 20
8,4,12
20, 10, 30
10, 20 15
In order for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
1. 8 + 8 = 16 < 20
8 + 20 = 28 > 8
8 + 20 = 28 > 8
The lengths 8, 8, and 20 do not form a triangle.
2. 4 + 8 = 12 > 4
4 + 12 = 16 > 8
8 + 12 = 20 > 4
The lengths 4, 8, and 12 do form a triangle.
3. 10 + 10 = 20 < 30
10 + 30 = 40 > 20
10 + 30 = 40 > 20
The lengths 10, 20, and 30 do form a triangle.
4. 10 + 15 = 25 < 20
10 + 20 = 30 < 15
15 + 20 = 35 > 10
The lengths 10, 15, and 20 do not form a triangle.