Exploring the Triangle Inequality Theorem

The video tutorial covers the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. It explains how to use this theorem to determine if given side lengths can form a triangle, using examples with specific measurements. A shortcut method is introduced to simplify the process by focusing on the two smallest sides. Additionally, the tutorial demonstrates how to find possible lengths for the third side of a triangle when two sides are known, using subtraction and addition to establish boundaries.

What does the Triangle Inequality Theorem state?

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

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

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

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

What happens if the sum of two sides of a triangle is equal to the third side?

• It forms a right triangle.

• It forms an equilateral triangle.

• It forms a straight line.

• It forms an isosceles triangle.

In the example with side lengths 5 cm, 6 cm, and 4.5 cm, what is the result of adding 5 cm and 6 cm?

• 10.5 cm

• 11 cm

• 9.5 cm

• 12 cm

Which combination of side lengths is checked first in the example with 5 cm, 6 cm, and 4.5 cm?

• 5 cm + 4.5 cm

• 6 cm + 4.5 cm

• 4.5 cm + 6 cm

• 5 cm + 6 cm

What is the shortcut method for checking if side lengths can form a triangle?

• Add all three sides together.

• Add the largest two sides and check if they are greater than the smallest side.

• Add the smallest two sides and check if they are greater than the largest side.

• Subtract the smallest side from the largest side.

If the two smallest sides of a triangle are 4 cm and 3 cm, can they form a triangle with a third side of 9 cm?

• No, because 4 + 3 is greater than 9.

• Yes, because 4 + 3 is equal to 9.

• No, because 4 + 3 is less than 9.

• Yes, because 4 + 3 is greater than 9.

What is the range of possible lengths for the third side if two sides of a triangle are 2 cm and 7 cm?

• Between 1 cm and 9 cm

• Between 2 cm and 7 cm

• Between 3 cm and 10 cm

• Between 5 cm and 9 cm

If two sides of a triangle are 12 cm and 5 cm, what is the smallest possible length for the third side?

• 6 cm

• 7 cm

• 8 cm

• 9 cm

If two sides of a triangle are 12 cm and 5 cm, what is the largest possible length for the third side?

• 19 cm

• 17 cm

• 16 cm

• 18 cm

What is the range of possible whole number lengths for the third side if two sides are 12 cm and 5 cm?

• 5, 6, 7, 8, 9, 10, 11, 12, 13

• 6, 7, 8, 9, 10, 11, 12, 13, 14

• 7, 8, 9, 10, 11, 12, 13, 14, 15

• 8, 9, 10, 11, 12, 13, 14, 15, 16