NOW FOR SOME GEOMETRY 

3rd year of secondary education 


1.
THE INTERIOR ANGLES IN A REGULAR
POLYGON


In
this window different regular
polygons appear when you change the parameter "n".
For practical reasons the highest value of "n" is 21. Look carefully at all the information given on the electronic board and
then complete the activities that follow.



1. Change parameter
"n" and
look at the different polygons that appear on the board. Then copy and complete the following table in your
exercise book:
2. Use
the information in the table above to try and work out the following for an
"n"sided polygon:
a. The
sum of the interior angles
b. The
size of an interior angle, in degrees.
3. Complete the following table:


4. Out
of all the polygons that you have seen on the electronic board for which
values of "n" was the interior angle a whole
number? Can you explain
why this is so?

2.
DIAGONAL LINES IN A REGULAR POLYGON


Different
types of regular polygons appear in this window, like in the window above.
However, this time diagonal lines inside the polygons are indicated. Remember that a diagonal line is a
segment which joins any two nonadjacent vertices in a polygon. In this case
the highest value of "n"
is fifteen as any values higher than this are too difficult to see clearly.



5. Look
carefully at the information given on the electronic board. Change the value
of "n" and copy and complete the following table in your exercise
book. (You decide on the number of rows):
6. How
many diagonals are there from each vertex in an "n"sided polygon?
How many diagonals are there altogether?
7. How
many diagonals are there from each vertex and altogether in regular polygons
with the following number of sides: 14, 25, 32 and 48?



3.
A STAIRCASE OF SQUARES


In
this window you can form a staircase with up to 8 steps, made by a series of
squares. Change the "steps"
parameter value and you will see how staircases of different heights appear.






4. A PYRAMID OF SEGMENTS 

In
this window you can see how a triangular shape is formed using segments. These
segments form small triangles which don't have a base. The "height"
parameter is equivalent to the "steps"
parameter in the exercise above.

























Josep Mª Navarro Canut 


ProyectoDescartes.org. Year 2013




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