Well to be able to solve problems of stereometry, at first it is necessary to study in detail its main figures – the planes, their properties and ways of construction. Let's consider a detailed algorithm of the solution of a widespread task of creation of the plane, to parallel set.
It is required to you
- - pencil,
- - ruler,
- - notebook, sheet of paper.
Instruction
1. Write a statement of the problem: to construct the plane passing through the set point of M parallel to this plane p. Always you remember the theorem according to which through the point which is not belonging to the set plane it is possible to carry out only one plane which will be parallel to this. It means that the correct drawing to each separate case will be only one.
2. Decision. So, let the point of M does not lie in this plane p. Then for the successful decision in this case it is necessary to carry out tasks consistently the following sequence of constructions: 1) In plane p draw two the crossed straight lines of a2 and a1;2) Through direct a1 and a point of M construct p1;3 plane) In p1 plane through a point of M draw the direct b1 parallel to direct a1;4) Through direct a2 and a point of M construct p2;5 plane) through a point of M carry out the direct b2 parallel to direct a2;6 To p2 planes) Through the crossed straight lines of b1 and b2 we carry out plane q. The turned-out plane q – required.
3. To solve a problem how to construct the plane parallel to set, it is possible also without implementation of the drawing. In the same cases when the drawing is carried out, it is necessary only to simplify work of imagination which can be insufficiently developed or when constructions are too difficult or bulky. Then creation of the correct drawing in this case is very important. Also for improvement of perception of a task it is possible all projective elements of a condition (points, straight lines, the planes) to transfer to material objects; walls, a floor and a ceiling of rooms are a good example.
4. The tasks similar to considered above, in the textbook are solved in the section on the subject "Parallel and Perpendicular Straight Lines and the Planes in Space", and their decision is most often limited only to creation of the drawing (at the same time there is no description, proofs, etc.) therefore many experience difficulties with tasks of this kind.