Create a Unique Triangle

The video tutorial addresses a math problem about forming unique triangles with given side lengths. It explains the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. The tutorial demonstrates checking this theorem with specific side lengths to confirm the formation of one unique triangle. It also notes that given only angles, multiple triangles can be formed, provided the angles sum to 180 degrees.

What is the first step in solving the problem of forming a unique triangle with given side lengths?

• Find the area of the triangle.

• Determine the angles of the triangle.

• Draw a picture of the triangle with the given side lengths.

• Calculate the perimeter of the triangle.

According to the Triangle Inequality Theorem, what must be true for any two sides of a triangle?

• They must be perpendicular to each other.

• They must be equal to the third side.

• They must be less than the third side.

• They must be greater than the third side.

Which of the following inequalities is NOT part of the checks for the given side lengths 2.5 cm, 6 cm, and 6.5 cm?

• 2.5 + 6.5 > 6

• 2.5 + 6 > 6.5

• 6 + 2.5 > 6.5

• 6 + 6.5 > 2.5

How many unique triangles can be formed with the side lengths 2.5 cm, 6 cm, and 6.5 cm?

• One unique triangle

• Two unique triangles

• Three unique triangles

• No unique triangles

If only the angles of a triangle are given, what must be true for the triangle to be valid?

• The angles must sum to 180 degrees.

• The angles must sum to 90 degrees.

• The angles must be equal.

• The angles must be less than 90 degrees.