# Construct an Equilateral Triangle 3

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

Worksheets for Geometry, Module 1, Lesson 2

Student Outcomes

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

Construct an Equilateral Triangle

Classwork

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?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 