6.5 Inequalities In One Triangle

Front

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

Back

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

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If two sides of a triangle are 5 in and 16 in, what is the range of possible lengths for the third side?

Back

11 in < x < 21 in.

Front

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

Back

Yes, it can.

Front

What is the condition for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

How do you determine the longest side in a triangle?

Back

The longest side is opposite the largest angle.

Front

What is the minimum length of the third side if two sides are 5 and 16?

Back

The minimum length is 11 (5 + 6 > 16).

Front

What is the maximum length of the third side if two sides are 5 and 16?

Back

The maximum length is 21 (5 + 16 > x).

Front

List the sides of a triangle from smallest to largest if the sides are 8, 9, and 16.

Back

8, 9, 16.

Front

Is it possible to construct a triangle with sides 9, 16, and 8?

Back

Yes, it is possible.