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 a triangle has sides of lengths 7 cm, 7 cm, and 7 cm, does it satisfy the Triangle Inequality Theorem?

Back

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

Front

Given sides of lengths 10 inches and 17 inches, what could be the length of the third side according to the Triangle Inequality Theorem?

Back

The length of the third side must be greater than 7 inches and less than 27 inches.

Front

Which of the following sets of lengths can form a triangle: 2 cm, 6 cm, 7 cm?

Back

Yes, because 2 + 6 > 7, 2 + 7 > 6, and 6 + 7 > 2.

Front

Can the lengths 15, 12, and 9 form a triangle?

Back

Yes, because 15 + 12 > 9, 15 + 9 > 12, and 12 + 9 > 15.

Front

What is an example of side lengths that do not form a triangle?

Back

3 cm, 10 cm, and 15 cm do not form a triangle because 3 + 10 is not greater than 15.

Front

If one side of a triangle is 5 cm and another is 8 cm, what is the range of possible lengths for the third side?

Back

The third side must be greater than 3 cm and less than 13 cm.

Front

What is the minimum length of a side in a triangle with sides 4 cm and 5 cm?

Back

The minimum length must be greater than 1 cm.

Front

If a triangle has sides of lengths 7, 7, and 7, what type of triangle is it?

Back

It is an equilateral triangle.

Front

What is the relationship between the sides of a triangle with lengths 8, 15, and 17?

Back

They satisfy the Triangle Inequality Theorem and form a triangle.