Constructing an equilateral triangle

Constructing an equilateral triangle using a compass and straightedge is really simple, as you probably know.

I feel it is a good project for students to explore and figure out how to do it. But here's how:

First you choose your side length. Here it is marked with the two dots.





Then you draw two circles, using the side length as the radius:




Where the circles intersect, is the third vertex of the triangle.



The beauty of this construction, I feel, is in how it exemplifies and applies the definitions of both circle and equilateral triangle.

You know, a circle is the set of those points that are at a given distance from the center point.

And an equilateral triangle is a triangle whose all sides have the same length.

This construction can help your student to truly grasp what these are. And it's simple enough.



After that, you would naturally introduce this problem:

Draw a triangle with given side lengths. For example, suppose you have these three 'sticks' or line segments given to you. Now draw a triangle.





The idea is exactly the same as before. But let them think about it and find it out. Can you figure it out?

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