Shape 

Copyright David & Cynthia Thomas, 2009

 

Necessary Conditions--Directed Activity: Euclid’s First Triangle, Part I

 

Focus

Construct an equilateral triangle

Technologies

·        Straightedge-and-compass

References

·        Euclid’s Elements Proposition 1

http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI1.html

·        Euclid of Alexandria

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

Background

For 2300 years, students of geometry have constructed geometric figures using straightedge-and-compass and justified the constructions using Euclidean logic.  This logic has, as its foundation, Euclid’s Five Postulates:

1.      A line segment may be drawn between any two points

2.      A line segment may be extended indefinitely in a straight line

3.      A circle may be drawn with any radius and any center.

4.      All right angles are congruent.

5.      If a straight line l intersects two straight lines m and n such that the interior angles on one side of l are together less than two right angles, then lines m and n intersect on that side of l (See Figure 1.3).

 

Figure 1.3: Euclid’s Fifth Postulate

 

Tasks

1.      Using straightedge-and-compass, construct an equilateral triangle (i.e., a triangle with three congruent sides). 

2.      Explain and justify the individual steps and final result of your construction.