# Cone Cross Sections Investigation

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 surface of a cone.

## Investigation Directions:

Attempt to answer the questions below before playing with the file here.Then move the points A, B, and C around on the surface of the cone.

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

2. What are the different cross section shapes which can be formed by moving points A, B, and C anywhere along the surface of the cone, being sure the 3 points are not collinear?

3. Which of the following polygons can be created by slicing a plane through a cone? (add a comment and explain your reasoning)

4. Would changing the height or radius of the cone affect your answers above? (add a comment and explain why, or why not?)