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 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Which of the following sets of lengths can form a triangle? 5, 5, 10

Back

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

Front

Which of the following sets of lengths can form a triangle? 6, 8, 10

Back

Yes, because 6 + 8 > 10, 6 + 10 > 8, and 8 + 10 > 6.

Front

What is the minimum length of the third side if two sides of a triangle are 7 and 10?

Back

The minimum length of the third side must be greater than 3 (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 and 10?

Back

The maximum length of the third side must be less than 17 (7 + 10).

Front

Can the lengths 12, 15, and 20 form a triangle?

Back

Yes, because 12 + 15 > 20, 12 + 20 > 15, and 15 + 20 > 12.

Front

If one side of a triangle is 8 and the other two sides are 3 and x, what is the range of possible values for x?

Back

x must be greater than 5 and less than 11.

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 a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because 5^2 + 12^2 = 13^2.