[color=#000000]Just as a line is made of an infinite number of points, a plane is made of an infinite number of lines that are right next to each other. A plane is flat, and it goes on infinitely in all directions. [/color][color=#000000][br][br][/color][color=#000000]A sheet of paper represents a small part of one plane. But actually a sheet of paper is much thicker than a plane, because a plane has no thickness. It is only as thick as a point, which takes up no space at all. So a plane is like an imaginary sheet of paper, infinitely wide and long, but with no thickness. [/color][color=#000000][br][br][/color][color=#000000]When we talk about a triangle or a square, these shapes are like pieces cut out of a plane, as if you had cut them out of a piece of paper.  But is there another way to create these polygons?[/color][color=#000000][br][br][/color][color=#000000]Some geometers are very interested what happens when a plane intersects or cuts a 3-Dimensional shape.[/color][color=#000000][br][br]Examine the [i]GeoGebra [/i]workspace.[br][br][/color][color=#000000]The light blue rectangle represents, like a piece of paper, a small part of a plane cutting through rectangular prism -- a cube.  The magenta shape represents the polygon that would be formed if the plane actually cut the cube.[/color][color=#000000][br][br][/color][color=#000000]Use the various sliders to experiment with different “slices” of the cube. Observe what polygons are created when a plane slices through a rectangular prism like a cube.[/color][color=#000000][br][br][/color][color=#000000]What shapes did you observe?  You should be able to construct a square, a rectangle, a triangle and a trapezoid.[/color][color=#000000][br][br][/color][color=#000000]Construct each of these polygons by slicing the cube with the plane.  Copy an image of each to the clipboard and paste the image into a Word file.  Print the Word file and add it to your Math Journal.[/color]