I draw the top half of a pattern first, and then draw the top half according to the characteristics of axisymmetric graphics, which becomes a complete pattern, and then I can design the edge of a poster by translation.
Symmetry and translation play a very important role in junior high school geometry or competition, and are one of the most important tools to solve plane geometry. Its knowledge is an important basis for us to study comprehensive topics in the future.
This section needs to master the characteristics of symmetrical and equal graphic transformation; Learn to use symmetry and translation functions to transform graphics. In this section, we solve some examples to introduce the common problems related to translation and symmetry in mathematics competitions and their solutions. This lecture will illustrate the application of these methods through examples.
Axisymmetric and axisymmetric graphics:
(1) has a graph folded along a straight line. If it can overlap with another figure, it is said that the two figures are symmetrical about this line, which is called the symmetry axis, and the point that overlaps after folding is the corresponding point, which is called the symmetry point. The symmetry of two graphs about a straight line is also called the symmetry axis.
(2) Axisymmetric figure: If a figure is folded along a straight line and the parts on both sides of the straight line can overlap each other, it is called an axisymmetric figure. This straight line is its axis of symmetry. (Symmetry axis must be a straight line)
(3) Symmetrical point: the overlapping point after folding is the corresponding point, which is called symmetrical point.
(4) Properties of axisymmetric figures: If two figures are symmetrical about a straight line, then the symmetry axis is the median vertical line of the line segment connected by any pair of corresponding points.
Similarly, the symmetry axis of an axisymmetric figure is the median vertical line of a line segment connected by any pair of corresponding points. The line segments connecting any pair of corresponding points are vertically bisected by the axis of symmetry, and the corresponding line segments are equal and the corresponding angles are equal on the axis of symmetry diagram.
(5) The step of drawing an axisymmetric figure about a straight line: find the key points, draw the corresponding points of the key points, and connect the points in the order of the original figure.