Triangle Inequality Theorem Concepts

This video tutorial explores the properties of triangles, focusing on the lengths of their sides and the angles between them. It introduces the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. The video provides examples to illustrate this theorem and discusses how changing the angles affects the side lengths. It also covers how to determine error intervals for the sides of a triangle. The tutorial concludes with a summary of the key concepts discussed.

What is the main topic discussed in the video?

• Quadrilaterals

• Polygons

• Triangles

• Circles

Which triangle is impossible based on the given side lengths?

• 5 cm, 9 cm, 15 cm

• 5 cm, 9 cm, 10 cm

• 5 cm, 9 cm, 20 cm

• 5 cm, 9 cm, 12 cm

What happens to the third side of a triangle as the angle between two sides increases?

• It becomes shorter

• It remains the same

• It becomes longer

• It disappears

What is the maximum length the third side can reach before it stops being a triangle?

• Greater than the sum of the other two sides

• Equal to the sum of the other two sides

• Less than the sum of the other two sides

• Equal to the difference of the other two sides

What happens to the third side of a triangle as the angle between two sides decreases?

• It disappears

• It becomes shorter

• It remains the same

• It becomes longer

What is the minimum length the third side can reach before it stops being a triangle?

• Equal to the difference of the other two sides

• Greater than the sum of the other two sides

• Less than the sum of the other two sides

• Equal to the sum of the other two sides

What does the Triangle Inequality Theorem state?

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

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

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

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

Which of the following is a correct application of the Triangle Inequality Theorem?

• a + b < c

• a + b = c

• a + b > c

• a + b ≤ c

If two sides of a triangle are 5 cm and 3 cm, what is the maximum possible length of the third side?

• 10 cm

• 9 cm

• 8 cm

• 7 cm

If two sides of a triangle are 7 cm and 10 cm, which of the following could be the length of the third side?

• 5 cm

• 9 cm

• 15 cm

• 18 cm