"Positional Similarity of Figures" Similarity of Figures PPT Courseware

Description

"Positional Similarity of Figures" Similarity of Figures PPT Courseware

Activity 1 Observation

In daily life, we often see similar graphics like this. For example, when showing a slide show, the graphics on the slide are enlarged onto the screen through the light source (the picture shows how it works).

Such enlargement and reduction does not change the shape of the graphics. The enlarged or reduced graphics are similar to the original graphics. Therefore, we can get real pictures and satisfactory photos.

Concepts and properties

1. Bit-like concept

If two figures are not only similar, but also the lines connecting the corresponding vertices intersect at a point and the corresponding sides are parallel to each other, then such two figures are called similarity figures, and this point is called a similarity center.

This point is called the position-like center,

The similarity ratio at this time is also called the position similarity ratio.

feature:

1. Similar shapes must be similar shapes, but not necessarily vice versa.

2. When judging similar shapes, please note that first they must be similar shapes, and secondly, the straight lines of each pair of corresponding points pass through the same point.

Explore

Is there any other way to solve the above problem? If you choose any point O outside the quadrilateral, take A', B', C' and D' on the reverse extension lines of OA, OB, OC and OD respectively,

What about making OA'/OA=OB'/OB=OC'/OC=OD'/OD=1/2? What if point O is taken inside quadrilateral ABCD? Draw the graphs obtained at this time.

We learned how to use coordinates to represent certain transformations such as translation, axial symmetry, and rotation (centrosymmetry) in a plane rectangular coordinate system. Similarity is also a transformation of graphics, and some special similarities (such as positional similarity) can also be represented by graphics. changes in coordinates.

induction:

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

The concept of bit-like graphics:

If two figures are not only similar in shape, but also the straight lines of each set of corresponding vertices pass through the same point, and the corresponding sides are parallel to each other, then such two figures are called similarity figures, and this point is called the similarity center. At this time, the similarity ratio Also called position similarity ratio.

Properties of bit-like figures:

The ratio of the distances between any pair of corresponding points on the similarity figure to the similarity center is equal to the similarity ratio

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For more information about the PPT courseware "The Position of Graphics is Similar to the Similarity of Graphics", please click on the Similarity of Graphics ppt tag.

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Update Time: 2024-09-06

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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