Introduction, Kiselev's Geometry, Book I. Planimetry, Givental Alexander .

 Exercises.

1. Give examples of geometric solids bounded by one, two, three, four planes (or parts of planes).

Solution: A single plane, or two, or three planes cannot bound a geometric solid. At the minimum we would need four planes in order to bind a geometric solid.

5.* Give an example of a surface other than the plane which, like the plane, can be superimposed on itself in a way that takes any one given point to any other given point.

Solution: Another surface which, like the plane, can be superimposed on itself in the way mentioned above would be a curved surface. But while superimposing it on itself the surface can lead to deformation.

8.* Fold a sheet of paper and, using the previous problem, check that the edge is straight. Can you explain why the edge of a folded paper is straight?

Solution: In the previous problem we had to check that the line passing through two given points on a sheet of paper is straight. We checked it by folding the sheet of paper long the line. Given that the line forms a hinge along which the sheet gets folded and given that the line coincides with the hinge exactly we can be sure that the line is straight.

This hinge or the line along which the paper gets folded is straight because a sheet of paper can be imagined as an approximation to a geometric plane surface. And a geometric plane surface can be imagined or assumed to be composed of straight lines. Thus, the edge of the folded paper is straight.

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