5.6 Inequalities in One Triangle

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

Can a triangle be formed with sides of lengths 5, 7, and 12?

Back

No, because 5 + 7 is not greater than 12.

Front

What is the condition for three lengths to form a triangle?

Back

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 8 and 10, what is the range of possible lengths for the third side?

Back

The third side must be greater than 2 and less than 18.

Front

What does it mean if the sum of two sides of a triangle equals the third side?

Back

It means that the three points are collinear, and thus, a triangle cannot be formed.

Front

Order the sides from greatest to least: 3, 5, 4.

Back

5, 4, 3.

Front

Can a triangle be formed with sides of lengths 7, 10, and 5?

Back

Yes, because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

What is the maximum length of a side in a triangle with sides 6 and 8?

Back

The maximum length is less than 14 (6 + 8).

Front

If one side of a triangle is 15, what is the minimum length of the other two sides combined?

Back

The minimum length must be greater than 15.

Front

What is the relationship between the longest side and the other two sides in a triangle?

Back

The longest side must be less than the sum of the other two sides.