Triangle Inequality Theorems

Front

What does the Triangle Inequality Theorem state about the lengths of the sides of a triangle?

Back

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Front

If one side of a triangle is longer than 8, what can we say about that side?

Back

The side length is greater than 8.

Front

How can you determine the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side.

Front

Given the side lengths 15, 12, and 9, does a triangle exist?

Back

Yes, a triangle with these side lengths exists.

Front

Where is the largest angle located in a triangle?

Back

The largest angle is located across from the longest side.

Front

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

Back

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

Front

What is the minimum requirement 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

If two sides of a triangle are equal, what can be said about the angles opposite those sides?

Back

The angles opposite the equal sides are also equal.

Front

What is the formula to check if three lengths can form a triangle?

Back

For lengths a, b, and c, check if a + b > c, a + c > b, and b + c > a.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

Lengths 5, 2, and 8 cannot form a triangle because 5 + 2 is not greater than 8.