Basic Constructions: Lesson 1 - Constructing an Equilateral Triangle

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Basic Constructions: Lesson 1 - Constructing an Equilateral Triangle
Honors Geometry

Learning Objectives You will learn to construct an equilateral triangle. You will communicate mathematic ideas effectively and efficiently.

Warm-up Point Line Line Segment Ray Plane
Term Example of Label Diagram Point Line Line Segment Ray Plane Italicized Capital Letter: D D Two capital letters with a line drawn over them: Two capital letters (called endpoints) with a segment drawn over them: Two capital letters with a ray symbol drawn over them:

Warm-up Solutions

Opening Exercise Joe and Marty are in the park playing catch. Tony joins them, and the boys want to stand so that the distance between any two of them is the same. Where do they stand? How do they figure this out precisely? What tool(s) could they use?

Reviewing Terms and Notation

Example 1: Sitting Cats Margie has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Place an M where Mack will be if the theory is true.

Example 1: Sitting Cats

Example 2: Examining Euclid’s Approach

Geometry Assumptions

Vocabulary

Vocabulary

Lesson Check We saw two different scenarios where the construction of an equilateral triangle was used to help determine a needed location. Describe another scenario where the construction of an equilateral triangle might be useful and articulate how you would find it.

Assignment Construct an Equilateral Triangle Worksheet

Follow the directions he/she wrote for #1 or #3. What kinds of difficulties did you have as you followed your classmate’s directions? Think about ways to avoid these difficulties. List at least 3 criteria or expectations for writing steps in constructions that should be included in a rubric for evaluating your writing.

Assignment Check

Assignment Check

Assignment Check

Assignment Check

Adding On… 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/or list of steps as needed.

Adding On… construct three equilateral triangles list the steps

Construct a Regular Hexagon
Use the skills that you have developed in this lesson to construct a regular hexagon. (Hint: A regular hexagon can be divided into 6 congruent equilateral triangles.) Clearly and precisely list the steps needed to accomplish this construction. Compare your results with a partner and revise your drawing and/or list of steps as needed.

Construct a Regular Hexagon
list the steps

What do you think? Why are circles so important to these constructions? Why did Euclid use circles to create his equilateral triangles in Proposition 1? How does constructing a circle ensure that all relevant segments will be of equal length?

Lesson Check Is the given triangle equilateral? Justify your response.

Assignment Segment Constructions Worksheet