Introduction to Polygons and Circle/Polygon Properties (According to my Excercise book)
ATTENTION!:This blog has been EDITED. Look for RED TEXT, indicated edited material.
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Volume 1:
"Introduction to Polygons"
The following Volume describes three different properties of a Polygon and how to find thier values.
Property 1: Number of Sides
Like the title says, one property of a Polygon is how many sides it has.
Property 2: Number of Triangles
Volume 1:
This property determines how many triangles the polygon can be divided into. So if you have a nice polygon like this:
You can divide it into many triangles like so:
And there is usually more than one way to make the triangles. If you're bored, try to find all the combinations for a polygon!
Property 3: Sum of the Angles
This property determines the total (sum) of each and every angle.
So how do all these properties relate to eachother?
They are related because each property can be used to find another. Meaning:
If you have the number of sides:
You can determine the amount of triangles with the following formula:
# of triangles = (n - 2)
Where "n" is the amount of sides.
You'll notice the above polygons follow this rule.
And, building upon that, you can determine the sum of the angles.
Sum of angles = 180t
Where "t" is the amount of triangles.
Solving for questions where you are given a different property just requires you rearrange your work a bit.
Ex. Find the amount of sides if the sum of the angles of a polygon is 1440 degrees.
->1440 = 180t
--> 1440 = 180(n - 2)
---> 1440 = 180n - 360
----> (1440 + 360)/180 = n
-----> 1800/180 = n
This is too tiring, you figure out the answer for yourself.
Anyway that pretty much wraps up this Volume.
Important details summary:
- Number of triangles = (number of sides - 2) or (sum of angles/180)
- Sum of angles = 180(number of sides - 2) or 180(number of triangles)
- Number of sides = (number of triangles + 2) or (sum of angles/180)+
"Inscribed angles with Tangents"
I just made up that name, because none of the "circle lessons" have had a title, and I felt this adequately described the lesson.
Anyway, lets get on with it.
We have a circle, chord tangents and two points like this:
Now lets connect these lines and create this nice litte mess here.
Now here's the part where we would normally measure the angles of GWU and GLU aswell as JGU and NGU. But since Windows doesnt have a protractor accessory (that would be cool), I'll just explain what should happen.
GWU + GLU = 180 just as JGU + NGU = 180 (its a straight line, makes sense). GWU = JGU and GLU = NGU. This is because they share an arc of GU.
[edit]
Even I am having trouble understanding what I just wrote, so if you don't understand it, ignore it. The main point is that the LEFT GU arc will be equal to twice the value of angle NGU and the RIGHT GU arc will equal twice the value of angle JGU. JGU is inscribed in the RIGHT GU arc, and NGU is inscribed in the LEFT GU arc. Very useful information, especially if you're stuck on question 2 of the Pretest.
[/edit]
And such ends this Volume and blog. Onward to picking the next scribe.
....eenie, meenie.... blah blah,
Almost two whole months without doing one!
Warning to bloggers: NEVER USE POINTY BRACKETS. EVER.
They are detected as HTML tags, and when I used them in my blog the lines using them got deleted. D:
Also, does anybody even add labels to thier posts?
And now I'm going to bed.
Labels: (n-2), arc, circle, polygon, properties
posted by Not Paul @ 10:35 PM
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