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Mathematical knowledge points of axial symmetry and central symmetry in the second day of junior high school
Review before class

1. There must be an axisymmetric figure () among the following geometric figures.

A.2 B.3 C.4 D.5

2. Among the following four playing cards, the one with the center symmetry is () in the figure.

3 In the following figures, the one that is both symmetrical and central is ().

A. isosceles trapezoid B. parallelogram C. regular triangle D. rectangle

4. Figures ① ~ ④ show four regular polygon tile patterns. Among them, the figure that is symmetrical but not central is ().

A.①③B.①④C.②③D.②④

Test site induction

1. If a graph is folded in half along a straight line, the folded ` two parts can be (), then the graph is (), and this straight line is its ().

2. If a graph is folded along a straight line, if it can be merged with another graph (), then these two graphs form (), this straight line is (), and the corresponding overlapping point after folding is ().

3. If two graphs are symmetrical about (), then the symmetry axis is () of any pair of line segments connected by corresponding points.

4. Rotate the graph around a certain point (). If the rotated graph can match the original graph (), then this graph is called () graph, and this point is its ().

5. Rotate the graph around a certain point (). If it can be connected with another graph (), then these two graphs are about this point (), and this point is called (). The corresponding points in these two graphs are called about the center ().

6. For two graphs with symmetric centers, the line segments connected by symmetric points both pass through () and are located in the symmetric center (). Two graphs with central symmetry are () graphs.

7. When two points are symmetrical about the origin, their coordinate symbol (), that is, the symmetrical point of the point about the origin is ().

Typical example

Example 1 As shown in the figure, there are three points on the square paper. It is required to make a quadrilateral so that three points are on the sides of the quadrilateral (including the vertices) and the vertices of the quadrilateral are on the vertices of the square.

(1) The quadrilateral in Figure A is a centrally symmetric figure, not an axisymmetric figure;

(2) The quadrilateral in Figure B is an axisymmetric figure, not a centrally symmetric figure;

(3) The quadrangle in Figure C is both an axisymmetric figure and a centrally symmetric figure.

2. The picture shows the Olympic flagpole logo, which consists of five circles with the same radius, symbolizing the unity and hard work of athletes from five continents. Then this mode ()

A.this is an axisymmetric figure. It is a figure with a symmetrical center.

C. it is not a symmetrical figure D. it is both an axisymmetric figure and a central symmetrical figure.

Xiaohua saw the clock on the wall behind him in the mirror. What time do you think is the closest to 8 o'clock?

4. If each letter in Figure 2 is regarded as an independent pattern, among the seven patterns, there is ().

1。

5. In the figure below, it is both an axisymmetric figure and a centrally symmetric figure ().