Triangle Inequality Theorem Concepts

The video tutorial introduces the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. It explains the three necessary inequality statements for a set of side lengths to form a triangle. The tutorial provides examples and non-examples to illustrate when side lengths can or cannot form a triangle, emphasizing the need for any two sides to be greater than the third.

What does the Triangle Inequality Theorem state about the sides of a triangle?

• The sum of the lengths of all three sides must be equal.

• The sum of the lengths of any two sides must be greater than the third side.

• The sum of the lengths of any two sides must be equal to the third side.

• The sum of the lengths of any two sides must be less than the third side.

Which of the following is a correct inequality statement for a triangle with sides a, b, and c?

• a + b ≤ c

• a + b > c

• a + b = c

• a + b < c

For a triangle with sides a, b, and c, which inequality must hold true?

• a + c < b

• a + c ≤ b

• a + c > b

• a + c = b

If two sides of a triangle are equal to the third side, what can be concluded?

• The sides will form an equilateral triangle.

• The sides will form a right triangle.

• The sides will form a triangle.

• The sides will not form a triangle.

What happens if the sum of two sides of a triangle is less than the third side?

• The sides will form a circle.

• The sides will not form a triangle.

• The sides will form a square.

• The sides will form a triangle.

In the context of the triangle inequality theorem, what is necessary for two sides to meet at a point?

• Their sum must be greater than the third side.

• Their sum must be less than the third side.

• Their sum must be twice the third side.

• Their sum must be equal to the third side.