Construct an Equilateral Triangle
You need a compass, a straightedge, and another student’s Problem Set. Directions: Follow the directions of another student’s Problem Set write-up to construct an equilateral triangle.
Exploratory Challenge 1
You need a compass and a straightedge.
Using the skills you have practiced, construct three equilateral triangles, where the first and second triangles share a common side and the second and third triangles share a common side. Clearly and precisely list the steps needed to accomplish this construction.
Switch your list of steps with a partner, and complete the construction according to your partner’s steps. Revise your drawing and list of steps as needed.
Construct three equilateral triangles here:
Exploratory Challenge 2
On a separate piece of paper, use the skills you have developed in this lesson construct a regular hexagon. Clearly and precisely list the steps needed to accomplish this construction. Compare your results with a partner, and revise your drawing and list of steps as needed.
Can you repeat the construction of a hexagon until the entire sheet is covered in hexagons (except the edges are partial hexagons)?
Why are circles so important to these constructions? Write out a concise explanation of the importance of circles in creating equilateral triangles. Why did Euclid use circles to create his equilateral triangles in Proposition 1? How does construction of a circle ensure that all relevant segments are of equal length?
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