Triangle Inequality and Inequalities

The video tutorial explains how to determine the possible range of values for the third side of a triangle using the triangle inequality theorem. It demonstrates that the sum of any two sides must be greater than the third side. By applying this principle, the tutorial derives that the third side, X, must be greater than 2 and less than 16, ensuring it is a positive value. The tutorial concludes by combining these inequalities into a compound inequality to define the range for X.

What is the main goal when finding the range of the third side of a triangle?

• To determine the exact length of the third side

• To find the possible range of values for the third side

• To calculate the area of the triangle

• To identify the type of triangle

Which theorem is used to find the range of the third side of a triangle?

• Cosine Rule

• Pythagorean Theorem

• Triangle Inequality Theorem

• Sine Rule

According to the triangle inequality theorem, what must be true about the sum of any two sides of a triangle?

• It must be twice the third side

• It must be less than the third side

• It must be equal to the third side

• It must be greater than the third side

If one side of a triangle is 7 and another is n, what must be true for the third side X?

• 7 + n < X

• 7 + n = X

• 7 + n ≤ X

• 7 + n > X

What inequality must be satisfied if X is added to 7?

• 7 + X ≤ 9

• 7 + X > 9

• 7 + X = 9

• 7 + X < 9

What inequality must be satisfied if X is added to 9?

• 9 + X ≤ 7

• 9 + X > 7

• 9 + X = 7

• 9 + X < 7

Why is the inequality 9 + X > 7 always true?

• Because X is zero

• Because X is a positive value

• Because X is a non-integer

• Because X is a negative value

What is the result when you add 7 and 9 in the context of triangle inequality?

• 16 is not related to X

• 16 is greater than X

• 16 is equal to X

• 16 is less than X

What is the result when you subtract 7 from 9 in the context of triangle inequality?

• X is greater than 2

• X is equal to 2

• X is not related to 2

• X is less than 2

What is the compound inequality that represents the range of the third side X?

• 2 > X > 16

• 2 = X = 16

• 2 ≤ X ≤ 16

• 2 < X < 16