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, 10 cm, and 15 cm, does it exist?

Back

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

Front

Which of the following sets of lengths can form a triangle: 7, 9, 19?

Back

No, because 7 + 9 is not greater than 19.

Front

What is the condition for three lengths a, b, and c to form a triangle?

Back

The conditions are: a + b > c, a + c > b, and b + c > a.

Front

Can a triangle exist with sides of lengths 15 cm, 12 cm, and 9 cm?

Back

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

Front

Identify a set of lengths that cannot form a triangle: 2 cm, 6 cm, 7 cm, 5 cm, 2 cm, 5 cm, 5 cm, 5 cm, 8 cm, 3 cm, 10 cm, 15 cm.

Back

3 cm, 10 cm, 15 cm cannot form a triangle.

Front

What is an example of a valid triangle with equal sides?

Back

An equilateral triangle with sides of length 7 cm.

Front

If the sides of a triangle are 7 cm, 7 cm, and 16 cm, does it exist?

Back

No, because 7 + 7 is not greater than 16.

Front

What is the minimum requirement for the lengths of two sides of a triangle?

Back

The sum of the lengths of the two sides must be greater than the length of the third side.

Front

What happens if the sum of two sides equals the third side?

Back

The lengths do not form a triangle; they are collinear.