### 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.

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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