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

If two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, the range is 2 < x < 12.

Front

Can the lengths 3, 4, and 8 form a triangle?

Back

No, because 3 + 4 is not greater than 8.

Front

What must be true about the lengths of 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

Given sides of lengths 6 and 10, what is the maximum length of the third side?

Back

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

Front

If the longest side of a triangle is 15, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 15.

Front

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

Back

The minimum length of the third side is greater than 2 (10 - 8).

Front

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

Back

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

Front

If one side of a triangle is 12, what is the range for the other two sides if they are both equal?

Back

The other two sides must be greater than 12 (12 - 12) and less than 24 (12 + 12). So, the range is 0 < x < 24.

Front

What is the relationship between the sides of a triangle when one side is much longer than the others?

Back

If one side is much longer than the sum of the other two sides, a triangle cannot be formed.