Triangle Inequality Theorem Problems

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

If the side lengths of a triangle are 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Can a triangle have side lengths of 2, 2, and 5?

Back

No, because 2 + 2 is not greater than 5.

Front

What is the minimum length of the third side if two sides of a triangle are 7 and 10?

Back

The minimum length of the third side must be greater than 3 (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 and 10?

Back

The maximum length of the third side must be less than 17 (7 + 10).

Front

If a triangle has sides of lengths 8, 15, and 17, is it a valid triangle?

Back

Yes, because 8 + 15 > 17, 8 + 17 > 15, and 15 + 17 > 8.

Front

What happens if the sum of two sides of a triangle equals the length of the third side?

Back

The figure is not a triangle; it forms a straight line.

Front

If one side of a triangle is 12 units and the other two sides are 5 units each, can this form a triangle?

Back

No, because 5 + 5 is not greater than 12.

Front

What is the relationship between the sides of a triangle and the Triangle Inequality Theorem?

Back

The lengths of any two sides must always be greater than the length of the third side.

Front

If a triangle has sides of lengths 6, 8, and x, what is the range of possible values for x?

Back

x must be greater than 2 and less than 14 (6 + 8 > x and 8 + x > 6, 6 + x > 8).