A, axisymmetric graphics
There are many kinds of symmetrical figures, such as axisymmetric figures: if a figure is folded in half along a straight line and the two parts overlap completely, such figures are called axisymmetric figures.
The axis of symmetry is a dotted line.
A straight line perpendicular to and bisecting a line segment is called the perpendicular bisector of the line segment, or the vertical centerline. The point on the vertical line in the line segment is equal to the distance between the two ends of the line segment.
In an axisymmetric figure, the corresponding points on both sides of the axis of symmetry are vertically bisected by the axis of symmetry.
Two symmetrical figures are congruent.
If two figures are symmetrical about a straight line, then the symmetry axis is the middle perpendicular of the line segment connected by any pair of corresponding points.
Second, the central symmetric figure
If a graph rotates 180 degrees around a certain point, and the rotated graph can completely coincide with the original graph, then this graph is called a centrosymmetric graph. And this center point is called the center symmetry point.
The line segments connected by each pair of symmetrical points on the central symmetric graph are equally divided by the symmetric center.
In a plane, if a graph rotates 180 degrees around a certain point, and the rotated graph can completely coincide with another graph, it is said that the two graphs form central symmetry. This point is called the symmetry center.
Common central symmetric figures are rectangle, diamond, square, parallelogram, circle and some irregular figures.
Even-numbered polygons are figures with symmetrical centers.
A regular odd polygon is not a centrally symmetric figure.
For example, a regular triangle is an axisymmetric figure, but not a centrally symmetric figure.
Supplement: The isosceles trapezoid is not a centrally symmetric figure, but an axisymmetric figure.
Third, the rotational symmetry graph
Rotationally symmetric figure: a figure rotates an angle around a fixed point, which is called the center of rotational symmetry, and the rotation angle is called the rotation angle. (The rotation angle is 0 degrees.
Common rotationally symmetric figures are: line segment, regular polygon, parallelogram, circle, etc.
Note: All centrally symmetric figures are rotationally symmetric figures.
Fourth, the error-prone points of symmetric graphics
Error-prone point 1: the concepts and properties of axisymmetric and axisymmetric figures, central symmetry and central symmetry figures are uncertain.
Error-prone point 2: To solve the problem of axial symmetry or rotation of a graph, we should make full use of its nature, that is, make use of the "invariance" of the graph to keep the size of the angle in axial symmetry and rotation unchanged and the length of the line segment unchanged.
Error-prone point 3: confuse axial symmetry and congruence, and confuse linear symmetry and axial symmetry.