Symmetry in geometry call ability of figures to display. In translation from Ancient Greek this word designates "harmony". There are several types of symmetry — mirror, beam, central, axial. Symmetric constructions are put in architecture, design and many other industries into practice.
It is required to you
- - properties of symmetric points;
- - properties of symmetric figures;
- - ruler;
- - square;
- - compasses;
- - pencil;
- - sheet of paper;
- - computer with the graphic editor.
Instruction
1. Carry out direct a which will be a symmetry axis. If its coordinates are not set, draw it randomly. On the one hand from this straight line put any end of A. it is necessary to find a symmetric point.
2. Remember what points are symmetric concerning an axis. Direct an in this case has to be a middle perpendicular to a piece between these points. That is to define location of a point In, it is necessary to carry out from a point And a perpendicular to an axis of symmetry and to continue it. To it designate a point of intersection of an axis and a perpendicular as the Lake.
3. From a point About lay off the distance equal to OA piece. Put the end of Century. It will be symmetric to a point And. If the straight line which is on the plane is set And, then each point which is on one its side is symmetric to only one point which is on other side from this straight line. Imagine rotation of the plane around this piece. If it turns on 180 °, then points And yes In will trade places.
4. In precisely the same way it is possible to construct also two symmetric geometrical figures. For example, the triangle of ABC to which it is necessary to construct symmetric is set. Carry out a symmetry axis. It can be set by statements of the problem. Their each top of the set triangle carry out perpendiculars to this straight line and prolong them for other party of the plane. Designate points of intersection as O, O1 and O2. From each of these points postpone pieces, equal OA, O1B and O2C. Connect the received points straight lines. In the same way it is possible to draw also other couples of symmetric figures.