Activity: To Triangle or Not to Triangle

Part 1 - Making Triangles
Below are 12 line segments (or straws) of various length. Make as many unique triangles as you can using these segments.



After you make your triangles, record them in the table below.

 

length A

length B

length C

What kind of triangle is it?
1        
2        
3        
4        
5        
6        


Part 2- Making “Untriangles”

We know that a triangle has three sides that form a closed shape. But what’s an "untriangle?"

Below is an example of an untriangle. Why do you think its called an untriangle?


Make and record your untriangles below:

 

length A

length B

length C

Why is this an untriangle?
1        
2        
3        
4        

Below are candidates for “trianglehood.” Indicate which are the triangles which are “wannabe” triangles (untriangles).

 

length A

length B

length C

Triangle (T) or
untriangle (U)?
Explain why T or U?
a 2 3 4    
b 8 4 2    
c 6 6 6    
d 7 4 3    
e 3 6 3    
f 8 6 6    
g 2 3 2    
h 2 5 2    
i 8 7 6    
j 3 4 5    

Some Questions:

1. If two of the two line segments are equal will you always be able to make a triangle with the third stick? Explain.


2. How about if all the segments are the same length? Can you always make a triangle? What is this triangle called?


3. Explain when it is possible for you to make a triangle with three segments.


4. Explain when it is NOT possible for you to make a triangle with three segments.