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 5 cm, 7 cm, and 10 cm, does it satisfy the Triangle Inequality Theorem?

Back

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

Front

What is the minimum length of the third side of a triangle if the other two sides are 8 cm and 6 cm?

Back

The minimum length must be greater than 2 cm (8 - 6).

Front

What is the maximum length of the third side of a triangle if the other two sides are 8 cm and 6 cm?

Back

The maximum length can be less than 14 cm (8 + 6).

Front

Can a triangle exist with sides of lengths 3 cm, 4 cm, and 8 cm?

Back

No, because 3 + 4 is not greater than 8.

Front

If the longest side of a triangle is 12 cm, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 12 cm.

Front

Which of the following sets of lengths can form a triangle? 5 cm, 5 cm, 10 cm; 7 cm, 10 cm, 12 cm; 3 cm, 4 cm, 8 cm.

Back

Only 7 cm, 10 cm, 12 cm can form a triangle.

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 one side of a triangle is 15 cm and the other two sides are 10 cm and 5 cm, can a triangle be formed?

Back

No, because 10 + 5 is not greater than 15.

Front

What is an example of a set of lengths that can form a triangle?

Back

Example: 6 cm, 8 cm, 10 cm.