Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the smallest angle in a triangle with sides 5, 12, and 13?

Back

The smallest angle is opposite the shortest side, which is 5.

Front

Given sides of lengths 7 and 10, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 and less than 17.

Front

If two sides of a triangle are 8 and 15, what is the minimum length of the third side?

Back

The minimum length of the third side must be greater than 7.

Front

Which set of numbers can represent the lengths of the sides of a triangle? {2,5,9}, {6,6,7}, {6,4,2}, {7,8,1}

Back

{6,6,7} satisfies the Triangle Inequality Theorem.

Front

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

Back

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

Front

How can you determine the smallest angle in a triangle?

Back

The smallest angle is opposite the shortest side.

Front

What is the maximum length of the third side if two sides are 8 and 15?

Back

The maximum length of the third side can be less than 23.

Front

If a triangle has angles of 30°, 60°, and 90°, which side is the longest?

Back

The side opposite the 90° angle is the longest.