# Slicing on an Angle

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Lesson Plans and Worksheets for Grade 7
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Examples, videos, and solutions to help Grade 7 students learn how to describe polygonal regions that result from slicing a right rectangular prism or pyramid by a plane that is not necessarily parallel or perpendicular to a base.

### New York State Common Core Math Grade 7, Module 6, Lesson 18

Worksheets for 7th Grade, Module 6, Lesson 18 (pdf)

### Lesson 18 Student Outcomes

• Students describe polygonal regions that result from slicing a right rectangular prism or pyramid by a plane that is not necessarily parallel or perpendicular to a base.

### Lesson 18 Summary

• Slices made at an angle are neither parallel nor perpendicular to a base (or, in the case of right rectangular prisms, a face).
• There cannot be more sides to the polygonal region of a slice than there are faces of the solid.
• Refer students to an interactive experience of “slicing” solids at the following Annenberg Learner website:

Lesson 18 Classwork

Example 1
a. With your group, discuss whether a right rectangular prism can be sliced at an angle so that the resulting slice looks like the figure in Figure 1? If it is possible, draw an example of such a slice into the following prism.

Exercise 1
a. With your group, discuss how to slice a right rectangular prism so that the resulting slice looks like the figure in Figure 2. Justify your reasoning.
b. With your group, discuss how to slice a right rectangular prism so that the resulting slice looks like the figure in Figure 3. Justify your reasoning.

Example 2
With your group, discuss whether a right rectangular prism can be sliced at an angle so that the resulting slice looks like the figure in Figure 4. If it is possible, draw an example of such a slice into the following prism.

Exercise 2
In Example 2, we discovered how to slice a right rectangular prism to makes the shapes of a rectangle and a parallelogram. Are there other ways to slice a right rectangular prism that result in other quadrilateral-shaped slices?

Example 3
a. Slicing a plane through a right rectangular prism so that the slice meets the three faces of the prism, the resulting slice is in the shape of a triangle; if the slice meets four faces, the resulting slice is in the shape of a quadrilateral. Is it possible to slice the prism in a way that the region formed is a pentagon (as in Figure 5)? A hexagon (as in Figure 6)? An octagon (as in Figure 7)?
b. Draw an example of a slice in a pentagon shape and a slice in a hexagon shape.

Example 4
a. With your group, discuss whether a right rectangular pyramid can be sliced at an angle so that the resulting slice looks like the figure in Figure 8. If it is possible, draw an example of such a slice into the following pyramid.
b. With your group, discuss whether a right rectangular pyramid can be sliced at an angle so that the resulting slice looks like the figure in Figure 9. If it is possible, draw an example of such a slice into the pyramid above.

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