Exploring the Triangle Inequality Theorem

What does the Triangle Inequality Theorem state?

• The sum of any two angles of a triangle must be greater than the third angle.

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

In the example with sides 9, 15, and 12, which pair of sides is checked first?

• 15 and 12

• None of the above

• 9 and 15

• 9 and 12

If a triangle has sides 4, 9, and 6, does it pass the Triangle Inequality Theorem?

• Yes, it passes.

• No, it does not pass.

• Only if the angles are right angles.

• Only if the sides are in a specific order.

What happens if one of the pairs of sides in a triangle does not satisfy the Triangle Inequality Theorem?

• The triangle becomes a right triangle.

• The triangle cannot exist.

• The triangle becomes an isosceles triangle.

• The triangle is valid.

How do you find the possible values of a missing side in a triangle?

• By subtracting and adding the given sides.

• By finding the average of the given sides.

• By multiplying the given sides.

• By dividing the given sides.

If the given sides of a triangle are 9 and 7, what is the range for the possible values of the third side?

• Between 2 and 16

• Between 1 and 16

• Between 1 and 14

• Between 2 and 14

For sides 8 and 5, what is the range for the possible values of the third side?

• Between 2 and 13

• Between 3 and 14

• Between 1 and 12

• Between 4 and 15

If the given sides are 11 and 2, what is the range for the possible values of the third side?

• Between 10 and 14

• Between 9 and 13

• Between 9 and 14

• Between 8 and 13

Why does the value of the missing side have to be greater than the difference and less than the sum of the given sides?

• To make the triangle a right triangle.

• To ensure the triangle is isosceles.

• To satisfy the Triangle Inequality Theorem.

• To ensure the triangle is equilateral.

What is the value of y if the given sides are 8 and 5?

• Between 4 and 15

• Between 1 and 12

• Between 3 and 14

• Between 2 and 13