Triangle Inequality Theorem

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

Does a triangle with side lengths 15, 12, and 9 exist?

Back

Yes, because 15 < (12 + 9), 12 < (15 + 9), and 9 < (15 + 12).

Front

What are the side lengths of an equilateral triangle?

Back

All sides are equal in length.

Front

If two sides of a triangle are 4 and 4, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 0 and less than 8.

Front

Identify the shortest side in a triangle with sides 5, 7, and 10.

Back

5 is the shortest side.

Front

Identify the largest angle in a triangle with sides 5, 7, and 10.

Back

The largest angle is opposite the longest side, which is 10.

Front

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

Back

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

Front

Can a triangle be formed with side lengths 2, 3, and 6?

Back

No, because 6 is not less than the sum of 2 and 3.

Front

What is the minimum length of a side in a triangle with sides 3 and 4?

Back

The minimum length must be greater than 1 (3 - 4 < x < 3 + 4).

Front

If a triangle has angles measuring 30°, 60°, and 90°, what type of triangle is it?

Back

It is a right triangle.