REQUIRED: you must do the Centroid,
Orthocenter,
Circumcenter, and Incenter - 25 points each.
Extra Credit: You may do as many as 4 additional constructions for extra credit
- only 3
extra credit constructions can be classical centers
- the other must be a 20th century center.
Carefully
choose centers that you can figure out how to
construct. Each completed extra credit construction (as
described below) is worth 5 points. Only two constructions can
be placed in any one grade category!
What to do:
1.
Pick
a triangle center from the ones above.
2.
Open
a Word document, (use the one at this link) and put your name
and hour in the area provided at the
top, create a folder called "triangle centers",
and
SAVE your document now in your triangle centers
folder on your network drive.
3.
In
the Word document, describe the triangle center that you will create-
-
how to construct
it,
-
at least 3 special properties or
interesting facts that the center has -
such as locations of the centers if they are different for acute, right and
obtuse triangles or any interesting
things about that center.
(i.e. for the centroid, it is an interesting to note that it
is the center of gravity for any triangle!) You may NOT use the
definition as a special property. You may have to go out to the
internet for more information to write about to get full credit in this
area.
4.
Using
Geometer's Sketchpad,
a. Construct an
acute triangle and measure the angles of the
triangle so that they show on your picture.
b.
Then
construct the center that you have
chosen. Make sure to label it with its name. (If you
create a centroid, label the point CENTROID on your sketchpad
drawing. )
c. When you
have
been successful, adjust your window on sketchpad to only view the triangle, its
angle measures, the lines that helped you find your center and MAKE SURE TO
INCLUDE THE CENTER, go to edit, choose select all, and then copy. Go back
to your Word document and paste the triangle center construction into your
Word document
.
d.
Pull and tug on the vertices of the triangle to make right and
obtuse triangles. See what effect the different triangles have on the location of the
special center that you are investigating. You will use this information
when writing the interesting things about your centers.
e. Drag your triangle to make it a right triangle and repeat the procedure
of copying and pasting it into your document as in part c.
e. Drag your triangle to make it an obtuse triangle and repeat the
procedure of copying and pasting it into your document as you did in parts c and
d.
f. If your constructions are too large, make them smaller so that each
center paper takes up no more than two pages when printed.
5.
At the bottom of the document
identify :
- whether this center is for extra credit or not
-
for any extra credit constructions, indicate the grade category - homework,
quizzes, tests, or labs - that you'd like those points put into, and
finally,
6.
Save
your completed document again in your own directory and
make sure that you name it with the center's name - don't leave any spaces in
the name - use a _ (underline) for a space! Save your sketchpad
file with the name of the center as well in the Triangle Centers Folder
on your network drive.
7. Hand in a print-out for each center that you construct.
