The mass of tasks is on the basis of properties of polyhedrons. Sides of volume figures, as well as concrete points on them, lie in the different planes. If to carry out one of such planes under a certain corner through a parallelepiped, then the part of the plane lying within a polyhedron and dividing it into parts will be its section.
It is required to you
- - ruler
- - pencil
Instruction
1. Construct a parallelepiped. Remember that its basis and each of sides have to represent a parallelogram. It means that you should construct a polyhedron so that all opposite edges are parallel. If in a condition is told to construct the section of a rectangular parallelepiped, then make its sides rectangular. At a straight line a parallelepiped only rectangular 4 side sides. If side sides of a parallelepiped are not perpendicular to the basis, then call such polyhedron inclined. If you want to construct cube section, initially draw a rectangular parallelepiped with equal sizes. Then all six of its sides will represent squares. Call all tops for convenience of designation.
2. Designate two points which will belong to the section plane. Sometimes their situation is specified in a task: distance from the next top, the end of the piece which is carried out on certain conditions. Now draw a straight line through the points lying in one plane.
3. Find straight lines on crossing of a secant of the plane with parallelepiped sides. For performance of this step find points in which the straight line lying in the parallelepiped section plane is crossed with the straight line belonging to a parallelepiped side. These straight lines have to be in one plane.
4. Complete parallelepiped section. At the same time you remember that its plane has to cross parallel sides of a parallelepiped on parallel straight lines.
5. Build a secant the plane according to basic data in a task. There are several opportunities of creation of the plane of section passing: - perpendicular to the set straight line through the set point; - perpendicular to the set plane through the set straight line; - parallel to two skew lines through the set point; - parallel to other set straight line through other set straight line; - parallel to the set plane through the set point. On such basic data build section by the principle described above.