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

Given three lengths, how can you determine if they can form a triangle?

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side for all three combinations.

Front

If the lengths of two sides of a triangle are 7 mm and 4 mm, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 mm and less than 11 mm.

Front

Can the lengths 15 in., 12 in., and 2 in. form a triangle? Why or why not?

Back

No, because 15 + 12 is not greater than 2.

Front

What is the minimum length the third side must be if two sides of a triangle are 10 inches and 17 inches?

Back

The minimum length of the third side must be greater than 7 inches.

Front

What is the maximum length the third side can be if two sides of a triangle are 10 inches and 17 inches?

Back

The maximum length of the third side can be less than 27 inches.

Front

If two sides of a triangle are 8 yd and 9 yd, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 1 yd and less than 17 yd.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, which of the following could be the length of side AC? 16 inches, 5 inches, or 30 inches?

Back

16 inches could be the length of side AC.

Front

What happens if the sum of two sides of a triangle is equal to the length of the third side?

Back

If the sum of two sides is equal to the length of the third side, the three points are collinear, and they do not form a triangle.

Front

What is the significance of the Triangle Inequality Theorem in real-world applications?

Back

The Triangle Inequality Theorem is used in various fields such as engineering, architecture, and computer graphics to ensure that structures and designs can physically exist.