For the sphere portfolio, you will need to do two at a time because of the
limited materials.
You should do the actual work for the portfolio on the overlays in the big plastic
box with the
red lid. Then sign your work.
Prep: Draw a "random" triangle ABC on one of the Lenart spheres
(the heavy ones in the cubical
boxes. You will use this as a basis for both constructions.
Then put a pair of overlays on the sphere, and copy the same triangle. Draw
the
complete great circles so that all 8 triangles are there. Then in the different
color, or
colors, construct all the 3 perpendicular bisectors (again, draw the entire
great circles) of
the sides of the original triangle ABC, check that they are concurrent visually,
and use this
to construct a circle through A, B, and C.
Then as a second phase, investigate the perpendicular bisectors of the other
sides. Figure out
how many distinct perpendicular bisectors there are.
Remove the overlays from #1 and put on a new set. Construct the POlAR TRIANGLE
of ABC on this new set. (Read Chapter 13 for the definition.)
The construct the angle bisectors of the polar triangle and check for concurrence.
Construct
the inscribed circle of the polar triangle
Again investigate and construct all the angle bisectors of the polar triangle.
Finally, figure out what the poles of the angle bisectors are, and how these
points are related
to the original figure in #1.
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Leave your work in the Math Study Center. I will check it on Wed and also from time to time.