Exploring Triangle Inequality with Different Lengths

The video tutorial covers the construction of triangles using physical objects and explores the conditions under which a set of three side lengths can form a triangle. It introduces the triangle inequality theorem, which states that the sum of any two side lengths must be greater than the third side length for a triangle to form. The tutorial includes practical examples and exercises to apply this theorem, and concludes with a discussion on making conjectures about triangle formation.

What is the base of the triangle in the initial example?

• Segment EF

• Segment CD

• Segment AB

• Segment BC

Which of the following sets of side lengths cannot form a triangle?

• 4, 5, 6

• 2, 3, 4

• 3, 4, 5

• 2, 3, 8

What must be true for three segments to form a triangle?

• The sum of any two side lengths must be equal to the third side length.

• The sum of any two side lengths must be greater than the third side length.

• The sum of any two side lengths must be less than the third side length.

• The sum of all three side lengths must be equal.

If you have sides of lengths 3, 4, and 9, can they form a triangle?

• Yes, because 3 + 4 is greater than 9.

• No, because 3 + 4 is not greater than 9.

• Yes, because 3 + 9 is greater than 4.

• No, because 4 + 9 is not greater than 3.

What is the Triangle Inequality Theorem?

• The sum of all three side lengths must be equal.

• The sum of any two side lengths must be equal to the third side length.

• The sum of any two side lengths must be greater than the third side length.

• The sum of any two side lengths must be less than the third side length.

Which of the following is true for a set of side lengths to form a triangle?

• The sum of any two side lengths must be equal to the third side length.

• The sum of all three side lengths must be equal.

• The sum of any two side lengths must be greater than the third side length.

• The sum of any two side lengths must be less than the third side length.

What happens if the sum of two side lengths is equal to the third side length?

• A circle is formed.

• A triangle is formed.

• A line segment is formed.

• A quadrilateral is formed.

Which of the following sets of side lengths will form a triangle?

• 3, 4, 9

• 5, 7, 13

• 24, 36, 42

• 1, 2, 4

What is a conjecture?

• A statement believed to be true

• A mathematical formula

• A proven theorem

• A geometric shape

If you have segments of lengths 6 cm, 7 cm, and an unknown length c, how many triangles can be formed?

• More than two

• Two

• One

• None