Shape 

Copyright David & Cynthia Thomas, 2009

 

Necessary Conditions--Directed Activity: Segment Lengths

 

Focus

Assemble a triangle from line segments

Technologies

·        The Geometers Sketchpad

·        Dry spaghetti

References

·        Euclid’s Elements Proposition 20

http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI20.html

·        Euclid of Alexandria

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html

Background

Figure 1.1 shows a model made with The Geometers Sketchpad of three triangles, each of which has a base of length 9.13cm.  The remaining two sides in each triangle are of different lengths. 

Figure 1.1: Segment Lengths

 

Tasks

1.      Using either The Geometers Sketchpad or dry spaghetti, investigate whether every set of 3 line segments may be joined to create a triangle.

2.      Justify your conclusions.