Triangle Inequality Theorem Concepts

The video tutorial explains how to determine if three given side lengths can form a triangle using the triangle inequality property. It provides three examples: 2, 3, 5 cm and 6, 3, 2 cm, which cannot form triangles, and 3, 6, 7 cm, which can form a triangle. The key concept is that the sum of any two sides of a triangle must be greater than the third side.

What is the main topic discussed in the video?

• How to calculate the area of a triangle

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

• How to find the perimeter of a triangle

• How to classify triangles by angles

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

• 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 all three sides must be equal

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

Which of the following is a correct application of the triangle inequality theorem?

• The sum of two sides is always equal to the third side

• The sum of two sides is always greater than the third side

• The sum of two sides is always twice the third side

• The sum of two sides is always 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 first example, what is the sum of the sides 3 cm and 5 cm?

• 8 cm

• 7 cm

• 9 cm

• 10 cm

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

• 6 + 3 is less than 2

• 6 + 2 is less than 3

• 3 + 2 is less than 6

• All combinations satisfy the theorem

In the second example, what is the sum of the sides 6 cm and 2 cm?

• 7 cm

• 10 cm

• 8 cm

• 9 cm

What is the result of the third example with sides 3 cm, 6 cm, and 7 cm?

• A triangle cannot be formed

• A triangle can be formed

• The sides are too long to form a triangle

• The sides are too short to form a triangle

In the third example, what is the sum of the sides 3 cm and 7 cm?

• 9 cm

• 10 cm

• 8 cm

• 11 cm

What is the key takeaway from the video regarding triangle formation?

• Only sides of equal length can form a triangle

• Any three sides can form a triangle

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

• The sum of all sides must be equal to form a triangle