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 two sides of a triangle measuring 10 and 8, what is the range of possible lengths for the third side?

Back

The third side must be greater than |10 - 8| = 2 and less than 10 + 8 = 18. Therefore, the range is (2, 18).

Front

If two sides of a triangle are 9 and 6, what is the minimum possible length for the third side?

Back

The minimum possible length for the third side is greater than |9 - 6| = 3, so it must be greater than 3.

Front

If two sides of a triangle are 8 and 9, what is the maximum possible length for the third side?

Back

The maximum possible length for the third side is less than 8 + 9 = 17, so it must be less than 17.

Front

What is an example of a value that cannot be the length of the third side of a triangle with sides 8 and 9?

Back

A value that cannot be the length of the third side is 17, as it does not satisfy the Triangle Inequality Theorem.

Front

How do you determine if a set of three lengths 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.

Front

What is the significance of the hint 'Build your range first' in triangle problems?

Back

The hint 'Build your range first' suggests calculating the minimum and maximum possible lengths for the third side based on the given sides, using the Triangle Inequality Theorem.

Front

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

Back

The Triangle Inequality Theorem establishes a relationship that must be satisfied for any three lengths to form a triangle.

Front

If one side of a triangle is 5 and another is 12, what is the range for the third side?

Back

The range for the third side is (7, 17), since it must be greater than |12 - 5| = 7 and less than 12 + 5 = 17.

Front

What happens if the lengths of the sides do not satisfy the Triangle Inequality Theorem?

Back

If the lengths do not satisfy the Triangle Inequality Theorem, the three lengths cannot form a triangle.