So today we did section 7.3 and 7.4, which are all about formulas involving polygons.
Lets start with 7.3
So Each polygon has a unique name (until you get up really high)
Sides: Polygon
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
15 Pentadecagon
n n-gon
Each polygon has a certain number of diagonals. These are formed when you connect different vertexes to eachother (except ones that form the outer edge of the shape)
The pink lines are the diagonals of this hexagon
The number of diagonals in a polygon can be found using
n(n-3)
# of diagonals= 2
(where n is the number of sides in the figure.)
You can also find the measure of all of the angles in a polygon using this formula:
sum of the angles= (n-2)180
This works because you can divide the shape into triangles with each triangle equaling 180 degrees.
See the triangles?
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The sum of the exterior angles of any polygon will ALWAYS be 360 degrees.
This is because if you start at one angle and slowly rotate around to the next angle, and the next and the next, you will have made a whole circle when you get back to the first, or 360 degrees!
We also learned a formula that isn't in the book, which is to find the measure of one angle of a shape with a certain number of sides.
180n-360
measure of one angle in an n sided polygon= n
Now for section 7.4
Section 7.4 focused on regular polygons. Here are examples of a few:
Regular Polygon- a polygon that is both equilateral and equiangular
They also showed some equiangular polygons, which are like regular ones but they dont necessarily have all sides congruent. (like a rectangle.)
A formula to find the measure of any exterior angle of an equiangular polygon:
360
measure of the exterior angle= n
And that was really all that we learned!
Random Math things:
NONAGON SONG! (click on it!)
Hope you liked the blog!!!!!!!!!!!
:) Katie
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