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
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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. |