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"Positional Similarity of Figures" Similarity of Figures PPT Courseware 3
one. Bit-like concept
If two figures are not only similar, but the straight lines of each set of corresponding vertices pass through the same point, and the corresponding sides are parallel to each other (or collinear), then such two figures are called similarity figures, and this point is called a similarity center, which is similar Ratio is also called bit-like ratio.
Notice
Positional similarity is a similarity with a positional relationship.
Similar figures are a special case of similar figures.
Similar figures must be similar figures, but similar figures are not necessarily similar figures.
There is only one similitude center of two similitude figures.
The two simulant figures may be located on either side of the simulant center, or they may be located on one side of the simulant center.
Bit-like properties
The corresponding point is collinear with the location center.
Corresponding sides that do not pass through the center are parallel.
The ratio of the distance between any corresponding point on the similarity figure and the center of the similarity is equal to the similarity ratio.
Determine whether the following pairs of figures are similar figures.
(1) Similar pentagon ABCDE and pentagon A’B’C’D’E’;
(2) Square ABCD and square A’B’C’D’;
(3) Equilateral triangle ABC and equilateral triangle A’B’C’.
Steps of similarity transformation
① Determine the positioning center, and the position of the positioning center can be selected at will;
② Determine the key points of the original figure. For example, a quadrilateral has four key points, that is, its four vertices;
③ Determine the similarity ratio. Based on the value of the similarity ratio, you can judge whether to enlarge or reduce a figure;
④The graphics that meet the requirements are not unique, because the graphics are related to the location of the determined location-like center, and there is a graphic that meets the requirements on both sides of the same location-like center.
Knowledge points
In the plane rectangular coordinate system, if the similarity transformation takes the origin as the similarity center and the similarity ratio is k, then the ratio of the coordinates of the corresponding points of the similarity figure is equal to k or -k, then the coordinates of the corresponding points on the image are ( kx, ky) or (-kx, -ky).
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