Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has side lengths of 5ft and 10ft, what is the range of lengths for the third side?

Back

5 < x < 15

Front

Can the side lengths 4, 5, and 10 form a triangle?

Back

No, because 4 + 5 is not greater than 10.

Front

What is the minimum length of the third side if two sides of a triangle are 8 and 6?

Back

The minimum length is 3 (8 - 6).

Front

What is the maximum length of the third side if two sides of a triangle are 8 and 6?

Back

The maximum length is 13 (8 + 6).

Front

If a triangle has sides of lengths 7, 10, and x, what must x be for a valid triangle?

Back

x must be between 3 and 17 (3 < x < 17).

Front

Can the side lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

What is the relationship between the sides of a triangle?

Back

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

Front

If a triangle has sides of lengths 9, 12, and 20, does it exist?

Back

No, because 9 + 12 is not greater than 20.

Front

What is the first step to determine if three lengths can form a triangle?

Back

Check if the sum of the two shorter lengths is greater than the longest length.