Sort into categories: Unique Triangles, Not Unique Triangles (Many Triangles), and No Triangle (Impossible).

Question

(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Unique Triangles Not Unique Triangles Impossible Triangles
Question 2
Give a brief explanation of how you sorted the above triangles. (1 point)

Answer 1

Unique Triangles:

1. Sets of three sides that follow the triangle inequality theorem and result in one specific triangle.
   • Example: Side lengths of 3, 4, and 5.

Not Unique Triangles:

1. Sets of three sides that can form multiple triangles based on the arrangement of angles or sides while still following the triangle inequality theorem.
   • Example: Side lengths of 5, 5, and 8 can create multiple isosceles triangles based on the angles.

Impossible Triangles:

1. Sets of three sides that do not meet the triangle inequality theorem requirements, making it impossible to form any triangle.
   • Example: Side lengths of 1, 2, and 3 (1 + 2 is not greater than 3).

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Brief Explanation for Sorting: I sorted the triangles based on the conditions of the triangle inequality theorem and the number of potential configurations they allow. Unique triangles are characterized by specific side lengths that form one distinct triangle. Not unique triangles can be formed in different configurations, while impossible triangles violate the fundamental properties needed to form a triangle altogether.