GEOMETRY FUNDAMENTALS

The Triangle

       A triangle is a shape with only 3 sides, or edges. Where two line segments meet is called a vertex. The plane that is created by a triangle is called a face. The bottom edge is called the base.


Let’s draw a triangle! First, we start with a line, then we make a bend and draw another line, then we make another bend and draw back to the starting line.

 

The next shape we will be exploring is the equilateral triangle. An equilateral triangle has 3 equal sides, with interior angles of 60 degrees on a plane.

The Circle-Triangle Relationship

Now we can explore the relationship between the circle and the triangle. Note the triangle surrounding the circle with a radius of 1:  The length of the side of the triangle is exactly 1.73 times the length of the incircle diameter

What makes the triangle interesting is that it is the most basic polygon which can enclose a space on a plane, and that is can be created from a circle (from the intersection of three, equally spaced lines tangent to the circle)

The circum circle is the circle that joins the outer triangle vertexes (where the bends are):

The triangle – circle relationship has amazing properties, first explored in by Pythagoras. Note how the radius of each circle is exactly twice that of the next smallest circle, and the height of each triangle is 2 times the preceding triangle as well.

 

 

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