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

Can the sides 5, 8, and 4 form a triangle?

Back

No, because 5 + 4 is not greater than 8.

Front

Can the sides 3, 10, and 8 form a triangle?

Back

Yes, because 3 + 8 > 10, 3 + 10 > 8, and 10 + 8 > 3.

Front

Can the sides 11, 12, and 9 form a triangle?

Back

Yes, because 11 + 9 > 12, 11 + 12 > 9, and 12 + 9 > 11.

Front

Can the sides 9, 6, and 5 form a triangle?

Back

Yes, because 9 + 6 > 5, 9 + 5 > 6, and 6 + 5 > 9.

Front

Can the sides 3, 6, and 2 form a triangle?

Back

No, because 3 + 2 is not greater than 6.

Front

What is the first condition of the Triangle Inequality Theorem?

Back

The sum of the lengths of any 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

If the sum of two sides equals the third side, the three points are collinear, and they do not form a triangle.

Front

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

Back

The sides 7, 10, and 5 can form a triangle because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

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

Back

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