This artifact is from Homework #6, Teaching Question #3. This week we were introduced to polygons and the different polygon rules. We were also introduced to angle sums and the different ways to find them. 

What is a Polygon?

A polygon is described as, "a simple, closed plane figure consisting of only line segments," for example, rectangles, squares, triangles, etc. 

Is a circle a polygon? The answer is no, because a circle is not made out of only straight-line segments, but rather it is made out of curve(s). 

Convex vs. Concave Polygons

There are two types of polygons, convex or concave. A polygon is described as convex, "if any line drawn through the polygon only enters and exits the polygon once," think of a square, when you draw a line through it, it enters at one side of the square and exits out the other, there are no gaps or holes. 

A polygon is described as concave if, "the polygon which is not convex is a concave polygon," or in other words, if you draw a line through the polygon and it enters and exits the figure more than once, it is concave. Think of a figure that has some sort of "dent" in it, or like a mountain range, if you were to draw a line through the mountains there would be gaps in between each peak. 

Interior Angle Sum of a Polygon

The interior angle sum of a polygon is the sum of all the interior angles of that polygon. To find the angle sum of a polygon you have to "cut" the polygon into triangles, because we know triangles have an angle sum of 180°, so we can then add the triangles you made together to find the angle sum of that polygon. However, you have to be careful when drawing the triangles within the polygon, they cannot just be randomly placed. They have to be connected to a vertex on the "edge" of the polygon (look at the drawing on the bottom of the picture to see the correct and incorrect way to draw these triangles). The equivalent formula is, (n-2) x 180°, where n represents the number of sides the polygon has. If the polygon is a regular polygon, which means all of the sides and angles are the same, then we know that we can reverse this process to find the interior angles of that polygon. You would take your interior angle sum and divide it by the number of sides the regular polygon has, and then you will have the interior angle measure of that polygon. 

My Understanding of Polygons (and tessellations)

I feel like a lot of the basics of polygons I had hidden way down deep in my memory from sometime in school when I was younger, however a lot of the information about angle sums and tessellations was new to me. At first determining what was actually a tessellation and what wasn't was a struggle for me. I remember doing the geometry scavenger hunt and finding so many things that were almost regular and semi-regular tessellations, but not quite, and it was really frustrating. However, now that I have seen more examples through work in and out of class, I am much more confident in my abilities to determine what is/isn't a tessellation. The other concept that I did struggle with was angle sums. I thought that I had it down, until we had to find the angle sum of two polygons put together, like a square and a rhombus for example, with only having one angle identified. Finding the angle sum of one regular polygon was easy, however finding the angle sum of multiple, not so easy. I still would consider that a point of confusion for me, I still get a little tripped up on those questions, however I am better than I was when I saw one for the first time.