Exploring the Triangle Inequality Theorem

The video tutorial covers 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 examples to determine if given side lengths can form a triangle and explores finding a possible third side for a triangle with two known sides. The tutorial emphasizes understanding and applying the theorem through practical examples.

What does the Triangle Inequality Theorem state?

• Any two sides added together should be less than the third side.

• Any two sides added together should be less than or equal to the third side.

• Any two sides added together should be equal to the third side.

• Any two sides added together should be greater than the third side.

Which of the following inequalities must be true according to the Triangle Inequality Theorem?

• a + c > b

• b + c < a

• a + b = c

• a + b < c

For the side lengths 3, 4, and 5, which inequality is correct?

• 3 + 4 > 5

• 3 + 5 < 4

• 3 + 4 < 5

• 4 + 5 < 3

Can the side lengths 3, 4, and 5 form a triangle?

• Only if 5 is the shortest side

• Yes

• No

• Only if 3 is the longest side

For the side lengths 6, 11, and 20, which inequality is false?

• 11 + 20 > 6

• 6 + 11 < 20

• 6 + 20 > 11

• 6 + 11 > 20

Can the side lengths 6, 11, and 20 form a triangle?

• Only if 6 is the longest side

• Only if 20 is the shortest side

• No

• Yes

For the side lengths 1, 2, and 3, which inequality is false?

• 1 + 3 > 2

• 2 + 3 > 1

• 1 + 2 > 3

• 1 + 2 = 3

Can the side lengths 1, 2, and 3 form a triangle?

• Only if 3 is the shortest side

• Only if 1 is the longest side

• No

• Yes

Given two sides of a triangle are 10 and 12, what is a possible range for the third side?

• Greater than 2 and less than 22

• Greater than 2 and less than 10

• Greater than 10 and less than 12

• Greater than 12 and less than 22

If the third side of a triangle with sides 10 and 12 is 10, what type of triangle is it?

• Equilateral

• Scalene

• Isosceles

• Right-angled