Triangle Inequality Theorem Concepts

Miss Li introduces the concept of triangle side lengths and the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. She provides examples to illustrate valid and invalid triangle formations and concludes with practice problems to reinforce the concept.

What is the main topic of today's lesson?

• Triangle angles

• Triangle side lengths

• Circle circumference

• Square area

Why is it important to take notes during the lesson?

• To draw better triangles

• To help with homework

• To improve handwriting

• To memorize theorems

What does the Triangle Inequality Theorem state?

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

• The sum of all sides is equal

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

• The sum of all angles is 180 degrees

Why are theorems important in mathematics?

• They are unproven ideas

• They are opinions

• They are guesses

• They are proven rules

How can the Triangle Inequality Theorem be simplified?

• The sum of the two longer sides is greater than the shorter side

• The sum of all sides is equal

• The sum of the two shorter sides is greater than the longer side

• The sum of the two shorter sides is less than the longer side

In the first example, what are the side lengths of the triangle?

• 4, 5, 7

• 6, 7, 9

• 3, 4, 5

• 5, 6, 8

Why do the side lengths 4, 5, and 7 form a triangle?

• 4 + 5 is less than 7

• 4 + 5 is less than 9

• 4 + 5 is equal to 7

• 4 + 5 is greater than 7

In the second example, why can't the side lengths 4, 2, and 7 form a triangle?

• 4 + 2 is equal to 7

• 4 + 2 is greater than 7

• 4 + 2 is less than 7

• 4 + 2 is greater than 6

What is the inequality statement for the side lengths 4, 2, and 7?

• 4 + 2 > 6

• 4 + 2 > 7

• 4 + 2 = 7

• 4 + 2 < 7

For the practice problem with side lengths 11, 6, and 13, what is the sum of the two shorter sides?

• 20

• 19

• 17

• 15