"Central Symmetry Figures" PPT Courseware 3

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"Central Symmetry Figures" PPT Courseware 3

Self-study: book p124

1. What is a centrally symmetrical figure? Center of symmetry? Symmetry point? How to verify that a figure is centrally symmetrical? for example.

2. What is centrosymmetry? Center of symmetry? Symmetry point?

3. What are the properties of two centrally symmetric figures?

definition

In a plane, a figure is rotated 180° around a certain point. If the figures before and after the rotation coincide with each other, then the figure is called a centrally symmetric figure, and this point is called its center of symmetry. The symmetrical points are called corresponding points.

think about it

Consider □ABCD as two triangles △ADC and △ABC,

(1) Are △ADC and △ABC centrally symmetrical?

(2) If △ADC and △ABC are centrally symmetric, then what are the line segments corresponding to the corresponding sides of line segments AD, DC, and AC respectively, and what are the corresponding points of points A, D, and C?

Apply properties to solve problems

1. How to create a symmetrical point at the center of the point

Taking point O as the center of symmetry, draw the symmetry point A′ of point A;

2. How to create a centrally symmetrical line segment

Taking point O as the center of symmetry, draw the symmetrical line segment point A′B′ of line segment AB.

central symmetry properties

(1) In two figures that are centrally symmetrical, the line connecting the corresponding points passes through the center of symmetry and is bisected by the center of symmetry.

(2) Any straight line passing through the center of symmetry divides this centrally symmetric figure into two parts with equal areas.

Consolidate and improve

Inheritance division problem: A rich man owned a piece of parallelogram land with a circular pond. The rich man made a will: he wanted to divide the land equally between his two sons, and the pond in the middle, but he didn't know how to do it. Can you think of a way?

analyze:

1. Is a parallelogram a centrally symmetrical figure? How to find the center of symmetry? What are the characteristics of a straight line passing through the center of symmetry?

2. What about round?

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"Central Symmetry Figures" PPT courseware 2:

"Central Symmetric Figures" PPT Courseware 2 Do it: Rotate the parallelogram 180 degrees around the intersection of the diagonals. What conclusion will you draw? Defined in the plane, a figure rotates 180 degrees around a certain point. If rotated The shapes before and after overlap each other, then this...

"Central Symmetry Figures" PPT courseware:

"Central Symmetric Figures" PPT courseware Observation Rotate the following figure 180 degrees around point O. What do you find? (1) Line segment (2) Circle (3) Parallelogram (4) Square The definition of centrally symmetrical figures is to rotate a figure 180 degrees around a certain point, such as...

"Central Symmetric Figures" Rotation PPT Courseware 3:

"Central Symmetry Figures" Rotation PPT Courseware 3 Review and Thinking (1) What are the common characteristics of these figures? They are all rotationally symmetrical figures. (2) What are the differences between these graphics? How many degrees did it rotate around the center of rotation? The rotation angle of the first shape is 12..

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Update Time: 2024-09-29

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

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