5-4 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

If a triangle has sides of lengths 5 and 13, what is the range of possible lengths for the third side?

Back

The length of the third side, x, must satisfy the inequality: 8 < x < 18.

Front

Can a triangle have sides of lengths 15 cm, 1 cm, and 15 cm?

Back

Yes, this triangle satisfies the Triangle Inequality Theorem.

Front

Which of the following cannot be the length of the third side of a triangle with sides 6 and 10? 5, 11, 15, 17

Back

17 cannot be the length of the third side.

Front

Which of the following cannot be the length of the third side of a triangle with sides 12 and 15? 2, 6, 12, 26

Back

2 cannot be the length of the third side.

Front

List the angles of a triangle from smallest to largest if the sides are 5, 12, and 13.

Back

The angles are:

Front

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

Back

In a triangle, the larger the side, the larger the opposite angle.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

What is the sum of the interior angles of any triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

How do you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: the sum of the lengths of any two sides must be greater than the length of the third side.