Triangle Inequality Theorem (Ordering and Forming Triangles)

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 lengths of two sides of a triangle are 10 inches and 17 inches, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 7 inches and less than 27 inches.

Front

What is the longest side in a triangle?

Back

The longest side in a triangle is the side opposite the largest angle.

Front

Can a triangle have sides measuring 5, 10, and 15?

Back

No, these sides cannot form a triangle because 5 + 10 is not greater than 15.

Front

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

Back

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

Front

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

Back

To determine if three lengths can form a triangle, check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is an example of a set of lengths that can form a triangle?

Back

An example is 3, 4, and 5, since 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What does it mean for a triangle to be degenerate?

Back

A degenerate triangle is one where the sum of the lengths of two sides equals the length of the third side, resulting in a straight line.

Front

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

Back

The longest side must be less than the sum of the other two sides to satisfy the Triangle Inequality Theorem.

Front

If a triangle has sides of lengths 9, 9, and 9, what type of triangle is it?

Back

It is an equilateral triangle, as all sides are equal.