Exploring the Triangle Inequality Theorem

This video tutorial covers the triangle inequality theorem, explaining how to determine if three sides can form a triangle. It demonstrates the theorem with examples, showing that the sum of the two shorter sides must be greater than the longest side. The tutorial also explores setting up inequalities for missing sides and applying these concepts in multiple choice questions. The video concludes with a preview of future topics related to triangle inequalities and angles.

What is the Triangle Inequality Theorem primarily used to determine?

• The area of a triangle

• The angles of a triangle

• If three sides can form a triangle

• The longest side of a triangle

If two sides of a triangle are 8 and 17, can the third side be 24?

• No

• Yes

• Only if it's a right triangle

• Only if it's an isosceles triangle

For a set of sides 25, 12, and 35, do they form a triangle?

• Yes, always

• Insufficient information

• No, never

• Yes, if arranged properly

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

• The shortest side must be shorter than the difference between the other two sides

• The longest side must be longer than the sum of the other two sides

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

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

In the context of the Triangle Inequality Theorem, what does a result of 'no' indicate?

• The sides form a perfect triangle

• The sides form a right triangle

• The sides cannot form a triangle

• The sides form an isosceles triangle

What is the range of possible values for the third side if two sides of a triangle are 14 and 22?

• Less than 22

• Exactly 36 or 8

• More than 14

• Less than 36 and more than 8

How can you determine the possible length of the third side given two sides of a triangle?

• By adding the two given sides

• By multiplying the two sides

• By using the sum and differences of the two sides

• By finding the average of the two sides

Given two sides of a triangle are 28 and 31, what is the smallest possible value for the third side?

• 28

• 59

• 3

• 31

What is the significance of the inequality 'x < 36 and x > 8' in the context of triangle sides?

• It represents the possible range for the third side of a triangle

• It indicates the maximum and minimum angles of a triangle

• It shows the only two possible lengths for the third side

• It is used to calculate the area of the triangle

If the lengths of two sides of a triangle are 15 and 27, which of the following could NOT be the length of the third side?

• 18

• 29

• 12

• 43