To determine corner size between skew lines, both straight lines are necessary (or one of them) to transfer to new situation by method of parallel translation before crossing. After that it is necessary to find corner size between the received crossed straight lines.
It is required to you
- Ruler, rectangular triangle, pencil, protractor.
Instruction
1. Modern technologies of various productions (constructions, mechanical engineering, instrument making, etc.) are based on creation of volume (three-dimensional) models. A basis of such construction is three-dimensional design (in a school course the solution of spatial tasks is considered in the section of geometry called stereometry). Quite often in three-dimensional design the solution of problems of definition of quantitative indices of a relative positioning of skew lines, for example, of distance and sizes of corners between them is required.
2. Skew lines are understood as such straight lines which do not belong to one plane. Corner size between two straight lines which are not belonging to one plane equals to corner size between two crossed straight lines, respectively parallel to these skew lines.
3. Therefore, to define a corner between two straight lines which are not belonging to one plane it is necessary to arrange straight lines parallel to them in one plane, that is to reduce a task to finding of a corner between two crossed straight lines (is considered in planimetry).
4. At the same time three options of arrangement of straight lines in space are absolutely equal: - the straight line parallel to the first straight line is carried out through any point of the second straight line; - the straight line parallel to the second straight line is carried out through any point of the first straight line; - the straight lines parallel to the first and second straight line are carried out through any point of space.
5. When crossing two straight lines two couples of adjacent corners are formed. The corner between two crossed straight lines is considered smaller of the adjacent corners formed when crossing straight lines (corners which sum is 180o are called adjacent). Measurement of a corner between the crossed straight lines brings in the solution of a task on corner size between skew lines.
6. For example, two direct an and b belonging different to the planes are given. On one of straight lines, let us assume, an is chosen any point And through which by means of a ruler and a rectangular triangle it is carried out direct b' in such a way that by b' | | b. According to the theorem of parallel translation the size of corners at such type of spatial movement is a constant. Thus, direct a forms with parallel direct b and b' equal corners. By means of a protractor we measure a corner between the crossed straight lines of an and b'.