Exploring Triangle Inequality Theorem Applications

Mr. Allen explains the triangle inequality theorem, which determines if three side lengths can form a triangle. He provides examples with different side lengths, demonstrating both valid and invalid triangles. The key rule is that the sum of any two sides must be greater than the third side. The video includes four examples, highlighting scenarios where triangles can and cannot be formed.

What is the purpose of the Triangle Inequality Theorem?

• To determine if three given side lengths can form a triangle

• To calculate the area of a triangle

• To determine if a triangle is right-angled

• To find the angles of a triangle

Given the side lengths 7, 9, and 15, can they form a triangle?

• Yes, because 7 + 15 is greater than 9

• No, because 9 + 15 is less than 7

• No, because 7 + 9 is less than 15

• Yes, because 7 + 9 is greater than 15

What must be true for any two sides of a triangle according to the Triangle Inequality Theorem?

• The sum of any two sides must be twice the third side

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

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

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

Given the side lengths 8, 6, and 15, why can't they form a triangle?

• Because 6 + 15 is less than 8

• Because 8 + 6 is less than 15

• Because 8 + 6 is greater than 15

• Because 8 + 15 is less than 6

What happens if the sum of two sides of a triangle is equal to the third side?

• They form an obtuse triangle

• They form an acute triangle

• They form a right-angled triangle

• They form a straight line

Given the side lengths 3, 7, and 10, why can't they form a triangle?

• Because 3 + 10 is less than 7

• Because 7 + 10 is less than 3

• Because 3 + 7 is greater than 10

• Because 3 + 7 is equal to 10

What is the result when the sum of two sides of a triangle is less than the third side?

• They cannot form a triangle

• They form a right-angled triangle

• They form an obtuse triangle

• They form an acute triangle

Given the side lengths 5, 5, and 7, can they form a triangle?

• No, because 5 + 7 is greater than 5

• No, because 5 + 5 is less than 7

• Yes, because 5 + 5 is greater than 7

• Yes, because 5 + 7 is less than 5

What is the key condition for the side lengths of a triangle to form a triangle?

• The sum of any two sides must be twice the third side

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

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

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

What should you do if your teacher asks for all combinations of side lengths?

• Show that the sum of any two sides is twice the third side

• Show that the sum of any two sides is less than the third side

• Show that the sum of any two sides is greater than the third side

• Show that the sum of any two sides is equal to the third side