"Central Symmetry" Rotation PPT Courseware 3

Description

"Central Symmetry" Rotation PPT Courseware 3

Scenario introduction:

(1) What do the following graphics have in common?

(2) Can you rotate these figures 1800 degrees around a point on them so that the figures before and after the rotation completely coincide?

Central symmetry: In a plane, a figure is rotated 1800 degrees around a certain point. If the figures before and after the rotation coincide with each other, then the figure is called a centrosymmetric figure, and this point is called its center of symmetry.

observe

(1) Rotate one of the patterns 180° around point O. What do you find?

(2) Line segments AC and BD intersect at point O, OA=OC, OB=OD. Rotate △OCD 180° around point O. What do you find?

concept

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 the point. It is also said that the two figures form central symmetry.

Knowledge points

1. For two figures that are symmetrical about the center, the line segments connected to the symmetry points all pass through the center of symmetry and are bisected by the center of symmetry.

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

Two basic properties of central symmetry:

(1) For two figures that are symmetric about the center, the lines connecting the corresponding points pass through the center of symmetry and are bisected by the center of symmetry.

(2) Two figures that are symmetric about the center are congruent figures and their applications.

1. Rotate △ABC around point O so that point A rotates to point D. Draw the rotated triangle and write down a brief method.

practice:

(1) Connect OA, OB, OC, and OD;

(2) Taking OB and OB as sides respectively, make ∠BOM=∠CON=∠AOD;

(3) Intercept OE=OB and OF=OC respectively;

(4) Connect DE, EF, and FD in sequence; that is: △DEF is the triangle you want to construct, as shown in the figure.

2. Quadrilateral ABCD is rotated 180° around point D. Please make the rotated pattern, write down the method and answer.

(1) Are these two figures centrally symmetrical? If it is the center of symmetry, which point is it? If not, please explain why.

(2) If it is centrally symmetrical, then what are the symmetrical points of A, B, C, and D about the center.

Solution: How to do:

(1) Extend AD and make DA′=AD

(2) Similarly: BD=B′D, CD=C′D

(3) Connect A′B′, B′C′, and C′D, then the quadrilateral A′B′C′D is the desired quadrilateral, as shown in the figure.

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For more information about the "Central Symmetry of Rotation" PPT courseware, please click the Rotation ppt Centrosymmetry ppt tag.

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Update Time: 2024-09-29

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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