"Central Symmetry Figures" PPT courseware

Description

"Central Symmetry Figures" PPT courseware

observe

Rotate the following figure 180° around point O. What do you find?

(1) Line segment (2) Circle

(3) Parallelogram (4) Square

Definition of centrally symmetrical figures

Rotate a figure 180° around a certain point. If the rotated figure can coincide with the original figure, then the figure is called a centrally symmetric figure, and this point is its center of symmetry.

summary:

1. Line segments, rectangles, rhombuses, squares, regular even-numbered polygons, and circles are not only centrally symmetrical figures, but also axis-symmetrical figures.

Parallelograms are centrally symmetrical figures, not axially symmetrical figures. Angles, isosceles triangles, equilateral triangles, and positive odd-numbered polygons are axially symmetrical figures, not centrally symmetrical figures.

2. Centrosymmetric figures have only one center of symmetry, while axial symmetry can have several different axes of symmetry.

3. If a figure is both an axially symmetrical figure and a centrally symmetrical figure, then the center of symmetry must be on the axis of symmetry.

Consolidation exercises

Multiple choice questions:

1. Which of the following figures is both an axially symmetrical figure and a centrally symmetrical figure ( ).

A angle B equilateral triangle

C line segment D parallelogram

2. Among the following polygons, which one is a centrally symmetrical figure instead of an axially symmetrical figure ( ).

A parallelogram B rectangle

C rhombus D square

Centrosymmetric

Rotate a figure 180° around a certain point. If it can coincide with another figure, then the two figures are said to be symmetrical about this point. Symmetry between two figures about a point is also called central symmetry. This point is called the center of symmetry.

As shown in the figure, △ABC and △A`B`C` are centrally symmetrical about point O, and point O is the center of symmetry.

As shown in the figure: the corresponding points A and A`, B and B`, C and C` are symmetric points about the center O.

Property 1 Two figures that are symmetric about the center are congruent.

∵ △ABC and △A`B`C` are centrally symmetric about point O

∴ △ABC≌ △A`B`C`

Property 2: For two figures that are symmetric about the center, the lines connecting the symmetry points pass through the center of symmetry and are bisected by the center of symmetry.

∵△ABC and △A`B`C` are centrally symmetric about point O

∴AA`, BB`, CC` pass through point O and OA=OA`, OB=OB`, OC=OC`

Centrosymmetric drawing

Example 1. Given point A and point O, draw the symmetry point A' of point A with respect to point O.

Connect OA and extend it to A’, so that OA’=OA,

Then A’ is the desired point

Example 2: Given line segment AB and point O, draw the symmetrical line segment A’B’ of line segment AB about point O.

Connect AO and extend it to A’, so that OA’=OA, then we get the symmetry point A’ of A

Connect BO and extend it to B’, so that OB’ = OB, then the symmetry point B’ of B is obtained

Connect A’B’, then the line segment A’B’ is the drawn line segment

Summary of rules

(1) To draw a point of symmetry about a certain point (center of symmetry), first connect the point to the center of symmetry and extend it twice as long.

(2) Draw a figure that is symmetrical about a certain point. The way to draw a figure is to first draw the symmetrical points of several special points in the figure (such as the vertices of polygons, endpoints of line segments, center points of circles, etc.) about a certain point, and then Just connect the relevant symmetry points in sequence.

Example 3: Given the quadrilateral ABCD and point O, draw the symmetrical figure of the quadrilateral ABCD about point O.

Art style:

1. Connect AO and extend it to A´, so that OA=OA´, and get the symmetric point A´ of point A.

2. Similarly draw the symmetry points B´, C´ and D´ of B, C and D.

3. Connect points A´, B´, C´ and D´ in sequence

Therefore, the quadrilateral A´B´C´D´ is the desired quadrilateral

Summary

Through today's study

1. What have you gained? What questions remain?

2. Do you know the difference and connection between axially symmetrical figures and centrally symmetrical figures?

move a square

(1) Make the resulting figure only an axially symmetrical figure;

(2) Make the resulting figure only a centrally symmetrical figure;

(3) It is both an axially symmetrical figure and a centrally symmetrical figure:

Explore further

How to determine whether two figures are centrally symmetrical about a certain point?

If the line segments connecting corresponding points of two figures pass through a certain point and are bisected by that point, then the two figures must be centrally symmetrical about this point.

Consolidation exercises

3. Known: The number of true propositions in the following propositions is ( ).

①Two figures that are symmetric about the center must not be congruent

②Two figures that are symmetrical about the center are congruent shapes

③Two congruent figures must be symmetrical about the center

A 0 B 1 C 2 D 3

4. Draw a figure as required. The drawn figure must have a square and a circle at the same time, and the figure must be both an axially symmetrical figure and a centrally symmetrical figure.

5. As shown in the figure, in the parallelogram ABCD, AC and BD intersect at point O, and the two straight lines passing through point O intersect each side at points E, H, F, and G respectively, then A, E, D, and G are about The symmetry points of O are _____, _____, _____, _____.

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Update Time: 2024-10-02

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 1 industry PPT template

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