a.
To explain: How to pass a plane through a cube so that the intersection is an equilateral
a.
Explanation of Solution
Given:
A cube and a plane.
An equilateral triangle cross-section can be obtained by cutting the cube by a plane defined by the midpoints of three edges emanating from any one vertex.
Conclusion:
Hence, an equilateral triangle cross-section can be obtained by slicing a cube.
b.
To explain: How to pass a plane through a cube so that the intersection is a trapezoid.
b.
Explanation of Solution
Given:
A cube and a plane.
A trapezoidal cross-section can be obtained by cutting the cube by a plane defined by the midpoints of two consecutive edges and the vertices just below the above edges.
Conclusion:
Hence, a trapezoidal cross-section can be obtained by slicing a cube.
c.
To explain: How to pass a plane through a cube so that the intersection is a pentagon.
c.
Explanation of Solution
Given:
A cube and a plane.
To get a pentagon, slice the cube with a plane going through five of the six faces of the cube.
Conclusion:
Hence, a pentagonalcross-section can be obtained by slicing a cube.
d.
To explain: How to pass a plane through a cube so that the intersection is an equilateral triangle.
d.
Explanation of Solution
Given:
A cube and a plane.
To get a hexagon slice with a plane going through all six faces of the cube.
Conclusion:
Hence, a hexagonal cross-section can be obtained by slicing a cube.
Chapter 7 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning