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Thursday, May 12, 2011

HW: Construction of a regular decagon!!

TODAY: I don't have your tests graded yet...but hopefully soon. I managed to give back some graded HW though- ya!

Today's activity involved many areas of math. We discussed the definition of regular polygons and then proceeded to investigate a few obvious properties of the regular decagon if it were inscribed in a circle. We drew the radii (segments from the center of the circle to the vertices of the decagon) of the decagon. We investigated one of those isosceles triangles.
It turns out that if the circle had a radius of 1 unit, then the side of the decagons would be equivalent to a very special number!!
We found this special length using the mentioned isosceles triangle, similar triangles, proportional side lengths, and the solution of a quadratic equation using the quadratic formula.

Then a nice construction with the compass and straightedge followed!!

All the steps are on the new handout from today!!
TRY the construction all over again on your own at home.
Good luck.

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