Triangle Inequalities

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

Back

The third side must be greater than |7 - 10| = 3 and less than 7 + 10 = 17. So, the range is (3, 17).

Front

What is the relationship between the angles and sides 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

If one side of a triangle is 5 and another is 8, what is the maximum length of the third side?

Back

The maximum length of the third side is 5 + 8 = 13.

Front

If one side of a triangle is 12 and another is 7, what is the minimum length of the third side?

Back

The minimum length of the third side is |12 - 7| = 5.

Front

What can be concluded if the sum of two sides of a triangle equals the length of the third side?

Back

If the sum of two sides equals the length of the third side, the three points are collinear, and thus, they do not form a triangle.

Front

In a triangle with sides 6, 8, and x, what is the range of possible values for x?

Back

x must be greater than |6 - 8| = 2 and less than 6 + 8 = 14. So, the range is (2, 14).

Front

What is the smallest angle in a triangle with sides 3, 4, and 5?

Back

The smallest angle is opposite the shortest side, which is 3.

Front

If a triangle has sides of lengths 9, 12, and x, what is the maximum value of x?

Back

The maximum value of x is 9 + 12 = 21.

Front

What is the minimum value of x in a triangle with sides 10, 15, and x?

Back

The minimum value of x is |10 - 15| = 5.