One of types of symmetry is central. The center of symmetry - some point of O concerning which rotate the plane, turning it on 180 °. Each point of A passes into such point of A' that O is AA midpoint'.
Instruction
1. If two points, by the center of symmetry between them, by definition are given, there will be a middle of the piece connecting them. More difficult the situation with a geometrical figure is: here it is already necessary to consider all points making it. Any any point has to pass in is central symmetric to it, otherwise the principle of symmetry will be broken.
2. If two figures about which it is told that they are symmetric rather unknown center are given, try to rotate each of figures mentally. As a result you have to present transition to 180 ° (half of circle). Find any two symmetric points, carry out between them a piece. In its center the center of symmetry and these two points, and all figure will be located.
3. Let it is necessary to construct the circle symmetric to O given concerning a point. The center of a circle let is designated by a point of C. Draw a straight line from a point of C through a point O. Legs of compasses measure OC distance, lay off the same distance on a straight line from O point in other party. Record result, it will be the center of a new circle. Measure by compasses the radius of an initial circle and complete symmetric.
4. To construct the polygon symmetric to given concerning center O, find an image of each of its tops. The starting point is called "prototype", final – "image". Consistently connect points among themselves. Mentally rotate figures, estimate whether the result turned out correct.
5. If the spatial figure is given, and it is necessary to find the center of symmetry between any two points, remember properties of this volume body. Perhaps, the center of symmetry lies on crossing of diagonals, bisectors, medians, perpendiculars. Prove that the point specified by you is nominal the center of symmetry, using properties of a figure, other data in a problem of a condition and determination of symmetry.