HansGeorg Weigand and James P. Dildine
The following links allow an exploration into new ways of
working with triangles that can be afforded to us through
technology.
We want you to explore the locus of special points of a triangle. We solve problems in five steps 




Go ahead with the following problems. Try to solve them first by your own. Afterward you will see the solution.
First: Given is the triangle ABC shown below (The point C should be on the parallel!). Point C moves along a line that is parallel to the line segment AB and the line the segment is contained in.
Problem 1: First step: You see the CIRCUMCENTER of a triangle ABC. If you move point C along the line parallel to base AC... What locus of points is created if C moves along the line parallel to the base. Do a hand draft of this locus. 
Second step: PICTURE were you can do a hand draft.
Third step: Next PICTURE (without perpendicular bisectors): Now you can move the point C. Also animate .....
Forth step: Why do you think that the formation created is as such? Write it down: TEXTBOX.
Fifth step: If you don't know it, you may also look at the next PICTURE (with perpendicular bisectors): Do you have an idea now, why. ...
????There is a possibility to go on e. g.
Problem 2: Now point C moves along a circle (or on another curve). ...... 
.........
Problem 3: Now we consider a quadrilateral (4sided polygon) ABCD. Construct the perpendicular bisectors of the quadrilateral ABCD 
This is a completely different problem....But this can lead to the classification of quadrilaterals.

The CIRCUMCENTER of a triangle results at the intersection of the perpendicualr bisectors of he sides of triangle ABC. You can construct the cirumcenter .....Back

Problem II: You see CENTER OF GRAVITY of a triangle ABC. If you move point C along the line parallel to base AC... What locus of points is created if C moves along the line parallel to the base. Do a hand draft of this locus. 
PICTURE were you can do a hand draft.
Next PICTURE (without perpendicular bisectors): Now you can move the point C. Also animate .....
Why do you think that the formation created is as such? Write it down: TEXTBOX.
If you don't know it: Do you know any property concerning the bisectors and the center of gravity.
Do you know what a dialation is? Now we do a dialation......
Problem 2: Now we consider a quadrilateral (4sided polygon) ABCD. Construct the perpendicular bisectors of the quadrilateral ABCD 
This is a completely different problem....But this can lead to the classification of quadrilaterals.

First step: The problem
Second step: Enactive level: Do it by hand
Third step: Do a computer animation
Forth step: Explain the computer picture
Fifth step: The computer as a help for explaining the problem.

The CIRCUMCENTER of a triangle results at the intersection of the perpendicualr bisectors of the sides of triangle ABC.
You can construct the cirumcenter .....