A Journey through Regular Polygons
Introduction
Do you know how many sides an octagon has? Do you know what common, everyday road sign is the shape of an octagon? What about a heptagon? How many sides does it contain and what are the sums of all of its angles? If one or all of these questions stumps you, well, they should J; you have yet to take Geometry!
In this WebQuest, you are going to search and seek out numerous types of regular polygons. [To start you off, I will define a polygon for you: A closed figure formed by three or more line segments that do not intersect other than at the vertices.] You are also going to be able to find out the sums of the angles of various polygons as well as construct your own polygons. Are you up to the challenge of discovering what types of polygons exist, what types of angles they have, be able to construct your own polygons? It is now up to you to discover the answers to these questions.
The Task
In
this WebQuest, you are going to learn all about regular polygons. You are going to search through various
websites to find information about various regular polygons. The things that you are to be looking for:
- Definition of a polygon and regular polygon
- Names of several types of regular polygons
- The sum of the angles of certain regular polygons
- For a regular polygon, the measure of each angle
- The number of diagonals that can be drawn from the vertices of any regular polygon
- The number of triangles formed by drawing diagonals from the vertices.
- Definition of a triangle and names of several types
- Measure of height of a triangle
The Process
1st Activity: Regular polygon, its
parts
Step 1.
The following link contains a lot of
information about polygons. However, all I want you to get from this website is
the definition of polygon and regular polygon, convex and concave polygon and
its parts (vertex, side, diagonal, interior angle, exterior angle). The site can be
used to help you on the other parts of this WebQuest.
Step 2.
For a more detailed explanation of
convex and concave polygon, you can also watch this video: https://www.youtube.com/watch?v=sWgHtiTSywc
Step 3.
Go to this link and draw a convex
and concave polygon. Copy your polygon and
paste it below:
Convex polygon
|
Concave polygon
|
Step 4.
Go to this other link and read
more about the parts of a polygon.
2nd Activity: Names of several regular
polygons
In this activity you will have to fill the
chart located bellow.
Step 1.
Please
click here. In this link, find the
name of the figures with the given number of sides and the sum if their
interior angles (also called sum of angles).
Once you find this information, put it in the chart. You must scroll down to view the names of
what you are looking for.
This
next set of instructions are designed for you to find the number of diagonals
that can be drawn from the vertices of any regular polygon, the number of
triangles created when you draw these diagonals, the formula for finding the
sum of the interior angles of a polygon, and the measure of each of the angles
in a regular polygons.
Step 1.
Click
here to determine how to find the sum of interior angles of a regular
polygon.
Step 2.
Using the above website (again, found
here), interpret from the example given how to determine how many lines can
be drawn from a given vertex for a given regular polygon. The example this website deals with a
pentagon. With a pentagon, choose a
vertex O (the definition is on the website) and then connect this vertex to all
of the other vertices using a single line to connect two vertices. Doing so will result in a pentagon having 4
lines connecting all of the vertices: OA, OB, OC, OD and OE (where A, B, C, D
and E are the labels for the exterior angles).
Step 3.
Using the following website,
find the Java applet that shows how many triangles are in each polygon. Use the more
and less buttons which are found
under the Number of Sides
located on the right of the page.
Now,
look at the following chart below and fill it.
Regular Polygon Chart
|
|||||
Name of Regular Polygon
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Number of Sides
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Number of Lines from any Vertex
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Number of Triangles
|
Sum of Interior Angles
|
Measures of each Regular Angle
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1.
|
3
|
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2.
|
4
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3.
|
5
|
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4.
|
6
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||||
7
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|||||
6.
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8
|
||||
7.
|
9
|
||||
8.
|
10
|
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9.
|
n-gon
|
||||
Step 1.
First, use this web
to analyse the different types of triangle, depending on its angles and
depending on its sides.
Step 2.
Find a triangle of each type in this link
and copy it here:
4th Activity: Height of a triangle and
apothem of a polygon
Step 1.
Finally, use this link
to learn what the height of any triangle is and for what is useful.
Step 2.
Measure the height of every triangle
you see in the English flag (use a just a rule to answer the question):
Step 3.
Go to this link, and learn what is the
apothem of any polygon. And fill in this table.
Apothem
of any polygon
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||
Polygon
|
Side
|
Apothem
|
Hexagon
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12
|
|
Square
|
12
|
|
Pentagon
|
5
|
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You can find this webquest in .doc here.
