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 must be greater than the length of the third side.

Front

Given the side lengths 47, 28, and 70, does a triangle exist?

Back

Yes, a triangle with these side lengths exists.

Front

Given the side lengths 20, 10, and 9, does a triangle exist?

Back

No, a triangle with these side lengths does not exist.

Front

Where is the largest angle of a triangle located?

Back

The largest angle is located across from the longest side.

Front

If two sides of a triangle are 8 feet and 11 feet, what is the smallest possible length of the third side?

Back

The smallest possible length of the third side must be greater than the difference of the two sides, which is 3 feet.

Front

What is the maximum possible length of the third side if two sides of a triangle are 8 feet and 11 feet?

Back

The maximum possible length of the third side must be less than the sum of the two sides, which is 19 feet.

Front

What is the Triangle Inequality Theorem used for?

Back

It is used to determine whether three given lengths can form a triangle.

Front

If one side of a triangle is 15 units and the other two sides are 10 units and 5 units, does a triangle exist?

Back

No, a triangle cannot exist because 10 + 5 is not greater than 15.

Front

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

Back

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

Front

How can you determine if 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.