Understanding the Triangle Inequality Theorem

The video tutorial explains the triangle inequality theorem, which states that the length of any side of a triangle must be less than the sum of the other two sides. The video provides a step-by-step example to verify if a given shape is a triangle by checking all three sides using this theorem. It emphasizes the importance of validating each side to confirm the shape is indeed a triangle.

What is the primary purpose of the Triangle Inequality Theorem?

• To measure the perimeter of a triangle

• To find the angles of a triangle

• To determine if a shape is a triangle

• To calculate the area of a triangle

According to the Triangle Inequality Theorem, what must be true about a single side of a triangle?

• It must be equal to the sum of the other two sides

• It must be greater than the sum of the other two sides

• It must be smaller than the sum of the other two sides

• It must be half the sum of the other two sides

In the example provided, what is the first side checked against the sum of the other two sides?

• Four

• Nine

• Five

• Three

What is the sum of the other two sides when the first side is left alone in the example?

• Eight

• Nine

• Five

• Four

When checking the second side of the triangle, what is the sum of the other two sides?

• Eight

• Seven

• Nine

• Ten

Which side is left alone when checking the second condition in the example?

• Four

• Three

• Nine

• Five

What is the result when the third side is compared to the sum of the other two sides?

• Five is not comparable to seven

• Five is less than seven

• Five is equal to seven

• Five is greater than seven

Why is it important to check all three sides of a triangle using the Triangle Inequality Theorem?

• To ensure the triangle is equilateral

• To confirm the triangle is valid

• To find the longest side

• To calculate the area

What happens if one of the conditions of the Triangle Inequality Theorem is not met?

• The shape is a circle

• The shape is still a triangle

• The shape is not a triangle

• The shape becomes a square

What is the final conclusion about the shape after all sides are checked?

• It is a circle

• It is a square

• It is a triangle

• It is not a triangle