Question
Consider the cross sections formed when slicing a shape by a plane parallel to its base.
This prism is sliced by a plane parallel to its base. What shape describes this cross section?
Rectangular prism sliced by a plane parallel to its base.
This cross section is a
.
Excellent!
This pyramid is sliced by a plane parallel to its base. What shape describes this cross section?
Hexagonal pyramid sliced by a plane parallel to its base.
This cross section is a
.
You got it!
Both of these cross sections are formed by slicing each shape by a plane parallel to its base. What do you notice about the two cross sections you just found?
Prism
Rectangular prism sliced by a plane parallel to its base. This prism's cross section is a rectangle.
Pyramid
Hexagonal pyramid sliced by a plane parallel to its base. This pyramid's cross section is a hexagon.
This prism is sliced by a plane parallel to its base. What shape describes this cross section?
Rectangular prism sliced by a plane parallel to its base.
This cross section is a
.
Excellent!
This pyramid is sliced by a plane parallel to its base. What shape describes this cross section?
Hexagonal pyramid sliced by a plane parallel to its base.
This cross section is a
.
You got it!
Both of these cross sections are formed by slicing each shape by a plane parallel to its base. What do you notice about the two cross sections you just found?
Prism
Rectangular prism sliced by a plane parallel to its base. This prism's cross section is a rectangle.
Pyramid
Hexagonal pyramid sliced by a plane parallel to its base. This pyramid's cross section is a hexagon.
Answers
GPT-4o mini
When a shape is sliced by a plane parallel to its base, the resulting cross section maintains the same shape as the base of the three-dimensional figure.
For example:
- When a rectangular prism is sliced by a plane parallel to its base, the resulting cross section is also a rectangle.
- When a hexagonal pyramid is sliced by a plane parallel to its base, the resulting cross section is a hexagon.
In both cases, the cross sections are similar in shape to the respective bases of the three-dimensional objects, demonstrating a property of solid figures that their cross sections will reflect the form of the base when cut parallel to it.
This leads to the general observation that slicing a prism or pyramid with a plane parallel to its base will yield a cross section that is similar in shape to the base of the solid.
For example:
- When a rectangular prism is sliced by a plane parallel to its base, the resulting cross section is also a rectangle.
- When a hexagonal pyramid is sliced by a plane parallel to its base, the resulting cross section is a hexagon.
In both cases, the cross sections are similar in shape to the respective bases of the three-dimensional objects, demonstrating a property of solid figures that their cross sections will reflect the form of the base when cut parallel to it.
This leads to the general observation that slicing a prism or pyramid with a plane parallel to its base will yield a cross section that is similar in shape to the base of the solid.