Hans-Georg 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.
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We want you to explore the locus of special points of a triangle. We solve problems in five steps |
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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.
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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.
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Problem 2: Now point C moves along a circle (or on another curve). ...... |
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Problem 3: Now we consider a quadrilateral (4-sided 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.
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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
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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......
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Problem 2: Now we consider a quadrilateral (4-sided 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.
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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.
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The CIRCUMCENTER of a triangle results at the intersection of the perpendicualr bisectors of the sides of triangle ABC.
You can construct the cirumcenter .....
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The CENTER OF GRAVITY OF A TRIANGLE is the intersection of the lines that make up the bisectors of sides triangle ABC.
If you move point B along the line parallel to the base AC then...What locus of points does this intersection point create? Draw a
picture on your own first and then use the interactive simulator here.
Center of Gravity (Median Center)