Triangle Inequality Theorem

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Yes, because 6 + 6 > 3, 6 + 3 > 6, and 6 + 3 > 6.

No, because 8 + 10 is not greater than 20.

Yes, because 6 + 5 > 8, 6 + 8 > 5, and 5 + 8 > 6.

Yes, because 6 + 10 > 8, 6 + 8 > 10, and 10 + 8 > 6.

No, because 9 + 12 is not greater than 22.

The lengths a, b, and c must satisfy: a + b > c, a + c > b, and b + c > a.

Yes, because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

No, because 3 + 4 is not greater than 8.

The three lengths will form a degenerate triangle, which is a straight line.