"Position Similarity" similar PPT courseware 5

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"Position Similarity" similar PPT courseware 5

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1.What is a bit-like figure?

If the straight lines of each set of corresponding vertices of two similar figures intersect at one point, then the two figures are called similarity figures, and the intersection point is called the similarity center. At this time, the similarity ratio of the two similar figures is also called their location. Similar.

Note: Two figures that meet the following two conditions at the same time are called positionally similar figures.

1. The two figures are similar.

2. The straight lines of each set of corresponding points pass through the same point.

Obviously, similarity figures are a special case of similar figures, and their similarity ratios are also called their similarity ratios.

2. What are the properties of position-like figures?

(1) The corresponding point of the similarity figure and the similarity center are on the same straight line.

(2) The ratio of the distance between any pair of corresponding points on the similarity figure to the center of the similarity is equal to the similarity ratio.

3. General steps for drawing bit-like figures:

1. Determine the positioning center

2. Connect and extend the approximate center and key points that represent the original image.

3. Based on the similarity ratio, determine the key points that can represent the similar shape.

4. Connect the above points in sequence to obtain an enlarged or reduced figure.

Explore 1:

In the plane rectangular coordinate system, there are two points A(6,3) and B(6,0), with the origin O as the similarity center, the similarity ratio is 1:3, and the line segment AB is reduced.

Observe the changes in coordinates between corresponding points. What do you find?

Exploration 2:

In the plane rectangular coordinate system, the coordinates of the three vertices of △ABC are A(2,3), B(2,1), and C(6,2). With the origin O as the similarity center, the similarity ratio is 2. △Enlarge ABC and draw its position-like shape.

What are the coordinates of the corresponding points after zooming in? What did you find?

A′( 4 ,6 ), B′( 4 ,2 ), C′( 12 ,4 )

induction:

In the plane rectangular coordinate system, if the similarity transformation takes the origin as the similarity center, and the similarity ratio between the obtained figure and the original figure is k, then the similarity ratio on the similarity figure corresponding to the point (x, y) on the original figure The coordinates of a point are (kx, ky) or (-kx, -ky).

Give it a try:

1. As shown in the figure, △ABC is reduced and △COD is obtained. Find their similarity ratio.

2. As shown in the figure, the coordinates of the three vertices of △ABC are A(2,-2), B(4,-5), and C(5,-2). With the origin O as the center, the triangle is enlarged as 2 times the original.

3. As shown in the figure, write the coordinates of each point of the rectangle wxyz. If the rectangle STUV is similar to wxyz, the coordinates of the point S are (2,2). According to the following similarity ratio, write the coordinates of the points T, U, and V respectively.

(1) The similarity ratio is 2; (2) The similarity ratio is 1/2;

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Update Time: 2024-10-05

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