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 the sides of a triangle are 3, 4, and 5, do they satisfy the Triangle Inequality Theorem?

Back

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

Front

Can the side lengths 2, 2, and 5 form a triangle?

Back

No, because 2 + 2 is not greater than 5.

Front

Identify the longest side in a triangle with sides 7, 10, and 5.

Back

10 is the longest side.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If a triangle has sides of lengths 6, 8, and x, what is the range of possible values for x?

Back

x must be greater than 2 and less than 14 (6 + 8 > x and x + 6 > 8 and x + 8 > 6).

Front

What is the smallest angle in a triangle with sides 5, 12, and 13?

Back

The smallest angle is opposite the side of length 5.

Front

List the side lengths of a triangle in order from shortest to longest: 9, 12, 15.

Back

9, 12, 15.

Front

Can the side lengths 1, 2, and 3 form a triangle?

Back

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

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.