Triangle Formation and Properties

The video tutorial explains how to determine if three given side lengths can form a triangle. It introduces the concept of triangle inequality, which states that the sum of any two sides must be greater than the third side. The tutorial provides examples to illustrate this rule and explains that the third side must be between the sum and the difference of the other two sides. The lesson concludes by combining these ideas into a single inequality and demonstrating its application with various examples.

What is the key concept introduced in determining if three sides can form a triangle?

• The sides must be in a geometric progression.

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

• The sides must all be equal.

• The sides must be in an arithmetic progression.

Why does the combination of sides 6, 8, and 20 not form a triangle?

• Because 20 is a prime number.

• Because 6 and 8 are too small to reach 20.

• Because 20 is less than the sum of 6 and 8.

• Because 6 and 8 are equal.

In the example of sides 6, 8, and 5, what type of angle is formed?

• Right angle

• Obtuse angle

• Straight angle

• Acute angle

What happens when the sum of two sides equals the third side, like in 6, 8, and 14?

• It forms a right triangle.

• It does not form a triangle.

• It forms an acute triangle.

• It forms an obtuse triangle.

Which of the following is true for a valid triangle?

• The sum of any two sides must be a multiple of the third side.

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

• 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.

What must the third side be greater than, according to the triangle inequality?

• The sum of the other two sides.

• The difference of the other two sides.

• The product of the other two sides.

• The average of the other two sides.

What is the significance of the difference between two sides in triangle formation?

• The third side must be a multiple of this difference.

• The third side must be equal to this difference.

• The third side must be greater than this difference.

• The third side must be less than this difference.

In the example of sides 6, 8, and 1, why does it not form a triangle?

• Because 1 is equal to the sum of 6 and 8.

• Because 1 is not between the sum and difference of 6 and 8.

• Because 6 is not between the sum and difference of 8 and 1.

• Because 8 is not between the sum and difference of 6 and 1.

What is the result when the third side is less than the difference of the other two sides?

• It forms a triangle.

• It forms a circle.

• It forms a straight line.

• It does not form a triangle.

What is the combined inequality for forming a triangle?

• The third side must be less than the difference of the other two sides.

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

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

• The third side must be less than the sum and greater than the difference of the other two sides.