68. General information on metric problems

The metric tasks are related to the determination of the true (natural) values ​​of distances, angles and flat figures in a complex drawing. There are three groups of metric tasks.

1. A group of tasks that include determining the distance from a point to another point; from point to line; from point to plane; from point to surface; from straight to other straight; from straight to plane; from the plane to the plane. Moreover, the distance from the straight line to the plane and between the planes is measured in cases when they are parallel.

2. A group of tasks, including the determination of angles between intersecting or intersecting straight lines, between a straight line and a plane, between planes (meaning the definition of the dihedral angle).

3. A group of tasks related to the determination of the true value of a flat figure and part of the surface (sweep).

The above problems can be solved using various methods of drawing transformation. The solution of metric problems is based on the property of rectangular projection, which consists in the fact that any geometric figure on the projection plane is projected in full size if it lies in a plane parallel to this projection plane. Problem solving is greatly simplified if at least one of the geometric figures involved in the tasks occupies a particular position. If one of the geometric figures does not occupy a particular position, it is necessary to carry out certain constructions that allow one of them to be held in this position.