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

Identify the smallest angle in a triangle with sides 5, 12, and 13.

Back

The smallest angle is opposite the shortest side, which is 5.

Front

Which of the following lengths cannot represent the sides of a triangle: 5, 10, 15?

Back

15 cannot represent the sides of a triangle because 5 + 10 is not greater than 15.

Front

What is the longest side in a triangle with sides 7, 24, and 25?

Back

The longest side is 25.

Front

Do the side lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 10.

Front

What is the relationship between the angles and sides of a triangle?

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

Can a triangle have sides of lengths 1, 2, and 3?

Back

No, because 1 + 2 is not greater than 3.

Front

What is the minimum length of one side of a triangle if the other two sides are 8 and 10?

Back

The minimum length must be greater than 2 (10 - 8).