#6.5 Inequalities in One Triangle

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

Can a triangle be formed with sides of lengths 15, 37, and 53?

Back

No, because 15 + 37 is not greater than 53.

Front

List the sides of a triangle with lengths 7, 12, and 10 from smallest to largest.

Back

7, 10, 12.

Front

What is the maximum possible length of the third side of a triangle with sides 7 and 12?

Back

The maximum length is less than 19 (7 + 12).

Front

What is the minimum possible length of the third side of a triangle with sides 7 and 12?

Back

The minimum length is greater than 5 (12 - 7).

Front

If a triangle has sides of lengths 12 and 15, which length cannot be the third side?

Back

2 cannot be the length of the third side.

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 8 and 10, which of the following can be the length of the third side? (Options: 5, 15, 12)

Back

12 can be the length of the third side.

Front

What is the order of sides in a triangle with lengths 5, 9, and 12 from smallest to largest?

Back

5, 9, 12.

Front

What is the minimum length of the third side of a triangle with sides 10 and 14?

Back

The minimum length is greater than 4 (14 - 10).