Lesson 5.4 Station 3

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

What are the conditions for three lengths to form a triangle?

Back

For three lengths a, b, and c to form a triangle, they must satisfy the conditions: a + b > c, a + c > b, and b + c > a.

Front

If two sides of a triangle are 2 and 6, what is the range for the length of the third side?

Back

The length of the third side must be greater than 4 and less than 8 (4 < x < 8).

Front

Which of the following sets of lengths can represent a triangle: {2, 5, 9}, {6, 6, 7}, {6, 4, 2}, {7, 8, 1}?

Back

Only the set {6, 6, 7} can represent the lengths of a triangle.

Front

What is the maximum length of the third side if the other two sides are 4 and 12?

Back

The maximum length of the third side is less than 16.

Front

What is the minimum length of the third side if the other two sides are 4 and 12?

Back

The minimum length of the third side is greater than 8.

Front

Which lengths cannot form a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

The lengths 28, 30, and 58 cannot form a triangle.

Front

What is an example of a set of lengths that can form a triangle?

Back

An example is {5, 5, 8}.

Front

What is the definition of a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides have different lengths.

Front

What is the definition of an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.