5-6 Inequalities In One Triangle

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 a triangle be formed with sides of lengths 15, 37, and 53?

Back

No, because 15 + 37 is not greater than 53.

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 12 and 15, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than |12 - 15| and less than 12 + 15, so it must be between 3 and 27.

Front

What is the smallest angle in a triangle?

Back

The smallest angle is located across from the smallest side.

Front

Can a triangle have sides of lengths 3 in, 6 in, and 2 in?

Back

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

Front

What is the maximum length of a side in a triangle with sides 12 and 15?

Back

The maximum length of the third side can be less than 12 + 15, which is 27.

Front

If a triangle has sides of lengths 12 and 15, which length cannot be the third side?

Back

2 cannot be the third side because 12 + 15 > 2, but 12 - 15 < 2.

Front

What is the sum of the angles in any triangle?

Back

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

Front

How do you determine the order of angles in a triangle?

Back

To determine the order of angles, compare the lengths of the sides: the smallest angle is opposite the shortest side, and the largest angle is opposite the longest side.