"Position Similarity" similar PPT courseware 3

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"Position Similarity" similar PPT courseware 3

1. What transformations of graphics have we learned before?

Symmetry (axial symmetry and axisymmetric graphics, central symmetry and central symmetric graphics): axis of symmetry, center of symmetry.

Translation: the direction of translation and the distance of translation.

Rotation: rotation center, rotation direction, rotation angle.

Similar: similar ratio.

Note: These different transformations of graphics are indispensable and important tools for us to learn geometry. It not only decorates our lives, but also is the basis for learning subsequent knowledge.

If two figures are not only similar, but the straight lines of each set of corresponding points 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 a similarity center.

Clear: similar, lines connecting corresponding points intersect at one point, corresponding sides are parallel

2. Properties of bit-like figures

Practice in class

1. The corresponding angles in two similar figures are ____, the corresponding line segments are _____, and the line connecting the corresponding vertices must pass through _______.

2. The distances between a pair of corresponding points on the similarity figure and the center of the similarity are 5 and 10 respectively, then their similarity ratio is ___.

review review

1.What is a bit-like figure?

If two figures are not only similar, but also the lines connecting the corresponding vertices intersect at a point, the two figures are called similarity figures, and this point is called the similarity center. The similarity ratio at this time is also called the similarity ratio.

2. 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

3. Use bitmap to enlarge or reduce a graphic

Can you get an upright enlarged "image", an upright reduced "image", or an inverted reduced "image"?

Exploration 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. Reduce the line segment AB.

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. Its position is like a figure.

What are the coordinates of the corresponding points after zooming in?

A′( 4 ,6 ), B′( 4 ,2 ), C′( 12 ,4 )

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.

What are the coordinates of the corresponding points after zooming in?

A′( -4 ,-6 ), B′( -4 ,-2 ), C′( -12 ,-4 )

Give it a try:

1. The figure shows △AOB and △COD obtained by reducing it, and 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, the coordinates of each point of the rectangle wxyz are known. 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.

So far, we have learned four transformations: translation, axial symmetry, rotation and similarity. Can you tell the similarities and differences between them? Can you find these transformations in the pattern shown?

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Update Time: 2024-11-26

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 2 industry PPT template

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