Show how to slice a cylindrical piece of cheese into eight congruent pieces with three slices.

To slice a cylindrical piece of cheese into eight congruent pieces with three slices, follow these steps:

Step 1: Cut the first slice
- Place the cylindrical piece of cheese on a cutting board.
- Position your knife vertically and cut the cheese horizontally across the top, creating the first slice. This slice should be parallel to the base of the cylindrical cheese.

Step 2: Rotate the cheese
- Gently pick up the cylindrical cheese and rotate it 45 degrees clockwise (or counterclockwise, as long as the rotation angle is consistent for the subsequent slices).
- Place the cheese back on the cutting board.

Step 3: Cut the second slice
- Once again, position your knife vertically and cut the cheese horizontally across the top, creating the second slice. This slice should also be parallel to the base of the cylindrical cheese.

Step 4: Rotate the cheese
- Repeat the same rotation process described in Step 2, but this time rotate the cheese 90 degrees clockwise (or counterclockwise) from its original position.
- Place the cheese back on the cutting board.

Step 5: Cut the third slice
- Position your knife vertically and cut the cheese horizontally across the top for the final time, creating the third slice. This slice should also be parallel to the base of the cylindrical cheese.

After following these steps, you will have three slices that divide the cylindrical piece of cheese into eight congruent pieces. Each slice creates two new congruent pieces, and the overlapping regions between the slices are also congruent.

Remember to exercise caution and use a sharp knife when slicing the cheese to ensure safety and achieve clean cuts.