How to build a plane that is parallel to a given

So good to be able to solve the problem of solid geometry, it is first necessary to examine in detail its basic shapes – plane, their properties and methods of construction. Consider the detailed algorithm for solving the common task of building a plane parallel to a given.

You will need

• pencil,
• - line
• - a notebook, a sheet of paper.

Instruction

1. Write a problem statement: build a planepassing through a given point M parallel to the given plane p. Always remember a theorem that States that through a point not belonging to the specified plane, it is possible to hold only one plane, which is parallel to this. This means that the correct drawing for each individual case will be only one.
2. Solution. Now, let the point M does not lie in the plane p. Then, for the successful solution of the problem in this case, you must execute the following sequence of constructions:1) In the plane p, draw two intersecting straight lines a2 and a1;2) Through the straight line a1 and the point M build a plane p1;3) In the plane p1 through the point M draw a straight line b1, parallel to the line a1;4) Through the straight line a2 and the point M build a plane p2;5) In the plane p2 through the point M draw a straight b2, is parallel to the line a2;6) Through intersecting straight lines b1 and b2 hold the plane q. The resulting plane q is desired.
3. To solve the problem of how to build a planethat is parallel to a given, and without a drawing. In those cases, when drawing is performed, it is needed only to simplify the work of imagination, which may not be sufficiently developed or when the build is too complex or cumbersome. Then build the right drawing in this case is very important. To improve the perception tasks, all projection elements (points, lines, planes) to transfer on material objects; a good example are the walls, floor and ceiling of the room.
4. Tasks similar to those considered above, in the textbook are solved in the section on "Parallel and perpendicular lines and planes in space", and their decision is most often confined to the creation of the drawing (in this case, there is no description, evidence, etc.), so many have difficulties with tasks of this type.