Triangle Inequality Theorem Flashcard

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.

No, a triangle cannot have a side length of 0.

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment. If GF = 4, then GC = 8.

No, they do not form a triangle because 2 + 2 is not greater than 4.

17 cannot be the third side because 6 + 10 is not greater than 17.

28, 30, and 58 cannot represent the sides of a triangle.

The minimum length of the third side must be greater than 4 (10 - 6).

The maximum length of the third side must be less than 16 (6 + 10).

x must be greater than 2 and less than 12 (5 + 7 > x and x + 5 > 7 and x + 7 > 5).

A degenerate triangle has side lengths that satisfy the equality in the Triangle Inequality Theorem, meaning the sum of two sides equals the third side.