Construct an Equilateral Triangle 3

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New York State Common Core Math Geometry, Module 1, Lesson 2

Worksheets for Geometry

Student Outcomes

  • Students apply the equilateral triangle construction to more challenging problems.
  • Students communicate mathematical concepts clearly and concisely.

Construct an Equilateral Triangle


Opening Exercise

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.

  • What kinds of problems did you have as you followed your classmate’s directions?
  • Think about ways to avoid these problems. What criteria or expectations for writing steps in constructions should be included in a rubric for evaluating your writing? List at least three criteria

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)?

Problem Set

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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