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 side lengths of a triangle are a, b, and c, what must be true according to the Triangle Inequality Theorem?

Back

The following inequalities must hold: a + b > c, a + c > b, and b + c > a.

Front

Do the side lengths 65 mm, 32 mm, and 33 mm form a triangle?

Back

No, because 65 mm is not less than the sum of 32 mm and 33 mm (65 >= 32 + 33).

Front

Which of the following measures DO NOT make a triangle: 5, 5, 11?

Back

These measures do not form a triangle because 5 + 5 is not greater than 11.

Front

Which side lengths form a triangle: 45, 40, 75?

Back

Yes, these lengths form a triangle because 45 + 40 > 75, 45 + 75 > 40, and 40 + 75 > 45.

Front

What is a necessary 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

Can the lengths 7, 9, and 5 form a triangle?

Back

Yes, because 7 + 9 > 5, 7 + 5 > 9, and 9 + 5 > 7.

Front

Do the lengths 4, 6, and 9 form a triangle?

Back

Yes, because 4 + 6 > 9, 4 + 9 > 6, and 6 + 9 > 4.

Front

What happens if one of the triangle inequalities is not satisfied?

Back

If one of the triangle inequalities is not satisfied, the three lengths cannot form a triangle.

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.