1. Basic Constructions: Lesson 2 - Constructing an Equilateral Triangle

2. Objectives Assessment
To apply basic construction of an equilateral triangle to more challenging problems
To communicate mathematic ideas effectively and efficiently using correct vocabulary
Assessment
Ticket out the door

3. Warm Up
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?

4. Vocabulary

5. Vocabulary

6. Vocabulary
Postulate: Suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief.
In geometry there are specific facts and definitions that we assume to be true.
Proposition: Something offered for consideration or acceptance

7. Geometry Assumptions

8. Examining Euclid’s Approach

9. 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.

10. 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.

11. 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?