Pyramid Cross Sections Investigation

Topic:
Pyramid
In the GeoGebra file below, use the tools to investigate the cross sections formed by slicing a plane through the three points located on the edges of the pyramid.

Investigation Directions:

Attempt to answer the questions below before playing with the file here.Then move the points K, M, and L around on the edges of the pyramid, also use the slider to change the base of the pyramid.

1. What is the shape of the cross section formed by slicing the pyramid above with the single plane through all three points K, M, and L? (Use the initial positions of points K, M, and L if you moved the points reset the GeoGebra file)

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2. What are the different cross section shapes which can be formed by moving points K, M, and L anywhere along the edges of each of the pyramid, being sure the 3 points are not collinear? (Change the base and see if it affects your answer)

3. What is the least number of sides a rectangular pyramid cross section shape can have?

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4. What is the greatest number of sides a rectangular pyramid cross section shape can have?

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5. Can you slice cross sections which form shapes with each of the numbers of sides in between the least and greatest number of sides? (Take pictures/screenshots of the above file as you investigate, showing each of the different cross sections you could find.)

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6. Describe how changing the base of the pyramid would affect your answers to questions 3, 4, and 5.