Determining Triangle Formation with Side Lengths

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 step-by-step examples to determine if given side lengths can form a triangle. The first example with sides 4, 4, and 7 forms a triangle, while the second example with sides 2, 4, and 6, and the third example with sides 3, 4, and 9 do not. The video concludes with practice problems for viewers to test their understanding.

What does the Triangle Inequality Theorem state?

• The sum of any two sides of a triangle must be equal to the third side.

• The sum of all three sides of a triangle must be equal.

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

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

In the first example, what are the two shortest sides?

• 4 and 7

• 4 and 4

• 7 and 4

• 4 and 8

What is the sum of the two shortest sides in the first example?

• 7

• 8

• 10

• 9

Why do the side lengths 2, 4, and 6 not form a triangle?

• Because 2 + 6 is equal to 4

• Because 2 + 4 is less than 6

• Because 2 + 4 is greater than 6

• Because 2 + 4 is equal to 6

What happens when you try to form a triangle with side lengths 2, 4, and 6?

• It forms a perfect triangle.

• It forms a square.

• It forms a straight line.

• It forms a circle.

In the third example, what is the sum of the two shortest sides?

• 9

• 8

• 7

• 6

Why do the side lengths 3, 4, and 9 not form a triangle?

• Because 3 + 9 is equal to 4

• Because 3 + 4 is greater than 9

• Because 3 + 4 is equal to 9

• Because 3 + 4 is less than 9

What is the result when you try to form a triangle with side lengths 3, 4, and 9?

• The sides never touch.

• The sides form a square.

• The sides form a straight line.

• The sides overlap perfectly.

Which of the following side lengths will form a triangle?

• 5, 5, 12

• 1, 2, 3

• 2, 2, 4

• 3, 4, 5

Which of the following side lengths will not form a triangle?

• 3, 4, 5

• 6, 7, 8

• 2, 2, 4

• 5, 6, 7