"Central Symmetry of Figures" PPT Courseware 2

Description

"Central Symmetry of Figures" PPT Courseware 2

Knowledge link

1. Central symmetry, central symmetry

Rotate a figure 180° around a certain point in a plane. This change in the figure is called central symmetry, and this fixed point is called the center of symmetry. If a figure can coincide with another figure through central symmetry, it is said that the two figures are about this fixed point. Be centrally symmetrical.

2. Basic properties of central symmetry

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.

think about it

(1) What characteristics do these graphics have in common?

(2) Rotate the "windmill" on the picture 180° around its upper point. Do the figures before and after the rotation completely coincide?

After the graphic is rotated 180° around a certain point, it completely overlaps with the original graphic.

induction:

If a figure can overlap with the original figure after being rotated 180° around a point, then the figure is called a centrosymmetric figure; this point is called its center of symmetry; the points that overlap each other are called symmetry points.

In a plane, a figure can coincide with the original figure through central symmetry. This figure is called a centrally symmetric figure.

Practice in class

1. 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 rather than an axially symmetrical figure ( )

A. Parallelogram B. Rectangle C. Rhombus D. Square

2. Decide whether the following statements are correct.

(1) Axisymmetric graphics are also centrally symmetrical graphics. ( )

(2) Rotational symmetrical figures are also centrally symmetrical figures. ( )

(3) Parallelograms, rectangles and squares are all centrally symmetrical figures, and the intersection of the diagonals is their center of symmetry. ( )

(4) An angle is an axially symmetrical figure and a centrally symmetrical figure. ( )

(5) In two centrally symmetrical figures, the corresponding line segments are parallel (or on the same straight line) and equal. ( )

give it a try

The side length of square ABCD is 1. The diagonals AC and BD intersect at point O. Another square EFGO that is congruent to it rotates around point O. OE, OG, AB, and BC intersect at point P and point Q respectively.

(1) What do you think is the relationship between △APO and △BQO?

(2) Try to find the area of ​​the overlapping part of the two squares. Does the area of ​​their overlap change during rotation? If it doesn't change, can you find out how much it is?

Entering the high school entrance examination

1: (2010 Qingdao, Shandong) Among the following figures, the centrally symmetrical figures are ( ).

2. (2013 Bijie) The following figures are both axis-symmetric figures and

The centrally symmetrical figure is ()

① Line segment, ② Angle, ③ Equilateral triangle, ④ Circle,

⑤ Parallelogram, ⑥ Rectangle.

A. ③④⑥ B． ①③⑥ C． ④⑤⑥ D． ①④⑥

What did you learn today?

1. Review the activities of this lesson.

Observe – analyze – explore – generalize – apply

2. What knowledge did you learn in this lesson?

(1) Definition of centrally symmetrical figures

(2) Properties of centrally symmetrical figures

(3) Which of the polygons we have learned are centrally symmetrical figures?

(4) Application of central symmetry graphics

Keywords: teaching courseware on central symmetry of graphics, Qingdao edition eighth grade mathematics volume 2 PPT courseware download, eighth grade mathematics slide courseware download, central symmetry of graphics PPT courseware download, .PPT format;

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"Central Symmetry of Figures" PPT courseware:

"Central Symmetry of Figures" PPT courseware knowledge link The definition of rotation is to rotate a figure around a fixed point by a certain angle in a certain direction (counterclockwise or clockwise) in a plane. This transformation is called the rotation of the figure. This fixed point It's called spin...

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Update Time: 2024-10-19

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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