Triangle Inequality Theorem Concepts

The video tutorial explains how to determine if a triangle can be formed with three given side lengths. It introduces the triangle inequality property, which states that the sum of the lengths of any two sides must be greater than the third side. The tutorial provides three examples with different side lengths to illustrate the application of this property. In the first two examples, the conditions are not met, so a triangle cannot be formed. In the third example, all conditions are satisfied, allowing a triangle to be formed.

What is the main topic discussed in this video?

• How to find the perimeter of a triangle

• How to calculate the area of a triangle

• How to determine if a triangle can be formed with given sides

• How to classify triangles by angles

According to the triangle inequality theorem, what must be true for three sides to form a triangle?

• The sum of all three sides must be equal

• 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

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

In the first example, why can't a triangle be formed with sides 2 cm, 3 cm, and 5 cm?

• Because 2 + 3 is less than 5

• Because 2 + 3 is equal to 5

• Because 3 + 5 is less than 2

• Because 2 + 5 is less than 3

In the second example, which combination of sides fails the triangle inequality theorem?

• All combinations satisfy the theorem

• 6 + 3 > 2

• 3 + 2 > 6

• 6 + 2 > 3

In the third example, what is the result of adding the sides 3 cm and 6 cm?

• 11 cm

• 10 cm

• 9 cm

• 8 cm

Which of the following is a valid combination for forming a triangle?

• 2 cm, 3 cm, 5 cm

• 5 cm, 5 cm, 10 cm

• 6 cm, 3 cm, 2 cm

• 3 cm, 6 cm, 7 cm

What is the sum of the sides 6 cm and 7 cm in the third example?

• 11 cm

• 12 cm

• 14 cm

• 13 cm

In the third example, which side is the largest?

• 6 cm

• 3 cm

• 7 cm

• All sides are equal

What is the key takeaway from the third example?

• A triangle can be formed if all side sums are less than the third side

• A triangle can be formed if all side sums are equal to the third side

• A triangle can be formed if all side sums are greater than the third side

• A triangle can be formed if one side sum is less than the third side

What should always be true for a triangle to be formed?

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

• The sum of all three sides should be equal

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

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