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 the sides of a triangle are 7 cm, 7 cm, and 7 cm, do they satisfy the Triangle Inequality Theorem?

Back

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

Front

Can the lengths 2 cm, 6 cm, and 7 cm form a triangle?

Back

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

Front

Which of the following sets of lengths can form a triangle: {2, 5, 9}, {6, 6, 7}, {6, 4, 2}, {7, 8, 1}?

Back

Only {6, 6, 7} can form a triangle.

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 the sides of a triangle are 3 cm, 10 cm, and 15 cm, do they satisfy the Triangle Inequality Theorem?

Back

No, because 3 + 10 is not greater than 15.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

The lengths 1 cm, 2 cm, and 3 cm cannot form a triangle because 1 + 2 is not greater than 3.

Front

If a triangle has sides of lengths 5 cm, 5 cm, and 8 cm, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 5 + 5 > 8, 5 + 8 > 5, and 5 + 8 > 5.

Front

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

Back

The maximum length of the third side must be less than 9 cm (4 + 5).

Front

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

Back

The minimum length of the third side must be greater than 1 cm (5 - 4).