You will need

- Ruler, triangle, pencil, protractor.

Instruction

1

Modern technologies in various industries (construction, engineering, instrumentation, etc.) are based on the construction of three-dimensional (three-dimensional) models. The basis of such a construction is a three-dimensional design (in the school course the solution to spatial problems is considered in the section of geometry called solid geometry). Quite often in three-dimensional design required the solution of problems of quantification of the mutual arrangement of intersecting straights, for example, distances and angles between them.

2

Under crossed lines defined as straight lines which do not belong to the same plane. The angle between two straight lines that do not belong to the same plane, is equal to the value of the angle between two intersecting straight lines, respectively, parallel data skew lines.

3

Therefore, to determine the angle between two straight lines that do not belong to the same plane, it is necessary to arrange them parallel straight lines in the same plane, that is, to reduce the problem to finding the angle between two intersecting straight (viewed in plane geometry).

4

It is absolutely equitable are three variants of straight lines in space:

-a direct parallel to the first straight line, is conducted through any point of the second straight line;

-a direct parallel to the second straight line, is conducted through any point of the first straight;

-straight and parallel first and second straight, are conducted through arbitrary point of space.

-a direct parallel to the first straight line, is conducted through any point of the second straight line;

-a direct parallel to the second straight line, is conducted through any point of the first straight;

-straight and parallel first and second straight, are conducted through arbitrary point of space.

5

If two intersecting lines form two pairs of supplementary angles. The angle between two intersecting straight is considered the smaller of the adjacent angles, formed by the intersection of the straight lines (called adjacent angles whose sum is 180°). The measurement of the angle between intersecting straight leads to the solution of the problem of the magnitude of the angle between the crossed lines.

6

For example, the two belong to different planes a and b direct. On one of the lines, for example, choose a arbitrary point a, through which when using the ruler and a right triangle are holding direct b' such that b' || b. According to the theorem of parallel transport, the magnitude of angles in this type of spatial displacement is a constant. Thus, a video forms with parallel lines b and b' equal angles. Using the protractor measure the angle between intersecting straight a and b'.

Note

You should observe the accuracy of geometric constructions and measurement angle.

Useful advice

A better option is to build a direct parallel to one of the data direct, through any point of the second straight line.