This applet allows the student to design, then construct their own oblique pyramid. By clicking on and dragging the points, the student can change the figure. This builds a sense of ownership from the very start. As the students manipulate the figure, ask the questions:
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[Why will the figure not work if the line segments cross? Answer: If the line segments cross, part of the paper would have to be used twice, but exists only once.]
[Why will the figure not work if the dotted lines are on the outside? Answer: If the dotted lines are on the outside, that means that the entire piece of paper is part of the figure (you don't cut dotted lines). The whole paper can not be folded into an oblique pyramid.]
[How can you create a right square pyramid using this application? Answer: If the lines on the upper part are all exactly the same length, the figure is a right square pyramid.]
[(Advanced) If all the other points are left alone and only point [i]J[/i] is moved, why must it move in a straight line? Answer: Line segments EJ and GJ are to be taped together. If they are not the same length, the figure will not work. So, J must be equidistant from E and G. The set of all points equidistant from E and G is a line.]
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