Triangle Inequality and Side Lengths

The video tutorial reviews the triangle inequality theorem, explaining that the sum of the two shortest sides of a triangle must be greater than the longest side. It provides examples to determine if given side lengths can form a triangle and discusses how to find the range of possible lengths for a missing side. A shortcut method for calculating this range is also introduced.

What is the main topic introduced in the video?

• Triangle Inequality Theorem

• Pythagorean Theorem

• Area of Triangles

• Types of Triangles

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

• The longest side must be twice the length of the shortest side.

• All sides must be equal.

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

• The sum of the two shortest sides must be greater than the longest side.

In the example with sides 4, 6, and 9, why can these sides form a triangle?

• Because 4, 6, and 9 are all even numbers.

• Because 4 + 6 is less than 9.

• Because 4 + 6 is greater than 9.

• Because 4 + 6 is equal to 9.

What type of triangle is formed by sides 10, 10, and 15?

• Equilateral

• Right

• Scalene

• Isosceles

Why can't the sides 3, 4, and 7 form a triangle?

• Because 3, 4, and 7 are not consecutive numbers.

• Because 3 + 4 is greater than 7.

• Because 3 + 4 is less than 7.

• Because 3 + 4 is equal to 7.

When given two sides of a triangle, what is the first step to find the range of the third side?

• Add the two given sides.

• Subtract the two given sides.

• Multiply the two given sides.

• Divide the two given sides.

If one side of a triangle is 12 and another is 8, what is the minimum possible length for the third side?

• 6

• 5

• 3

• 4

What is the maximum possible length for the third side if the other two sides are 8 and 12?

• 19

• 18

• 20

• 21

What is the range of possible lengths for the third side if the other two sides are 8 and 12?

• Between 6 and 18

• Between 5 and 19

• Between 4 and 20

• Between 7 and 17

What is the shortcut method to find the range of the third side of a triangle?

• Add and subtract the two given sides.

• Find the average of the two given sides.

• Multiply and divide the two given sides.

• Square the two given sides.