Triangle Properties and Classification

The video tutorial explains the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. It provides an example to illustrate this concept and checks if given side lengths can form a triangle. The tutorial also touches on classifying triangles based on their angles and concludes with a brief mention of shortcuts.

What is the first step in determining if three sides can form a triangle?

• Measure the angles between the sides

• Apply the triangle inequality theorem

• Check if all sides are equal

• Ensure the sides are integers

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

What is the significance of the triangle inequality theorem in geometry?

• It is used to classify triangles by type

• It is used to find the angles of a triangle

• It determines if three sides can form a triangle

• It helps in calculating the area of triangles

In the example given, why do the sides 2, 2, and 8 not form a triangle?

• Because 2 + 2 is not greater than 8

• Because 2 + 8 is not greater than 2

• Because 8 + 2 is not greater than 2

• Because all sides are not equal

Which of the following sets of side lengths can form a triangle?

• 10, 1, 1

• 1, 2, 3

• 5, 5, 5

• 3, 4, 8

Which of the following sets of side lengths cannot form a triangle?

• 7, 10, 5

• 6, 8, 10

• 9, 9, 9

• 2, 2, 5

How do you verify if the sides 7, 14, and 16 can form a triangle?

• Check if 7 + 16 is less than 14

• Check if 7 + 14 is greater than 16

• Check if 7 + 14 is less than 16

• Check if 14 + 16 is equal to 7

What is the result of adding the sides 7 and 16 in the context of triangle verification?

• Less than 14

• Greater than 14

• Equal to 14

• Equal to 16

If a triangle has sides 16, 14, and 7, what is the sum of the longest two sides?

• 30

• 23

• 20

• 21

What is the result of adding the sides 16 and 14 in the context of triangle verification?

• Less than 7

• Equal to 7

• Equal to 16

• Greater than 7