Triangle Inequality Theorem

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

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of side AC?

Back

The length of side AC must be greater than 7 inches and less than 27 inches. Possible length: 16 inches.

Front

Which of the following 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

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the two shorter sides must be greater than 10.

Front

What is an example of side lengths that can form a triangle?

Back

Side lengths of 5, 7, and 9 can form a triangle because 5 + 7 > 9, 5 + 9 > 7, and 7 + 9 > 5.

Front

What is the minimum length of a side in a triangle if the other two sides are 8 and 10?

Back

The minimum length must be greater than 2 (10 - 8).

Front

If one side of a triangle is 15 and the other two sides are 10 and x, what is the range of possible values for x?

Back

x must be greater than 5 and less than 25.

Front

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

Back

The three points are collinear, and they do not form a triangle.