Triangle Inequality Theorem Flashcard

Front

What is the Triangle Inequality Theorem?

Back

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.

Front

Can a triangle have side lengths of 0, 11, and 12?

Back

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

Front

If G is the centroid of triangle ABC, what is the relationship between the segments GF and GC?

Back

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.

Front

Do the side lengths 2 inches, 2 inches, and 4 inches form a triangle?

Back

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

Front

Given side lengths of 6 and 10, which length cannot be the third side?

Back

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

Front

Which of these lengths cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

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

Front

What is the minimum length of the third side of a triangle with sides 6 and 10?

Back

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

Front

What is the maximum length of the third side of a triangle with sides 6 and 10?

Back

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

Front

If a triangle has sides of lengths 5, 7, and x, what is the range of possible values for x?

Back

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

Front

What does it mean for a triangle to be degenerate?

Back

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.