Triangle Inequalities

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

Given two sides of a triangle, how do you determine the range of possible lengths for the third side?

Back

To find the range of the third side (x), use the inequalities: |a - b| < x < a + b, where a and b are the lengths of the two given sides.

Front

If two sides of a triangle are 8 and 9, what is the range for the third side?

Back

1 < x < 17.

Front

If two sides of a triangle are 6 and 10, what is the range for the third side?

Back

4 < x < 16.

Front

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

Back

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

Front

How do you list the angles of a triangle in order from smallest to largest?

Back

Order the angles based on the lengths of the opposite sides, from shortest to longest.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Front

What is the range of the third side if the two sides are both 9?

Back

0 < x < 18.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is always opposite the largest angle.

Front

How can you determine if a set of three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side.