"Positional Similarity of Figures" Similarity of Figures PPT Courseware 2

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"Positional Similarity of Figures" Similarity of Figures PPT Courseware 2

Observe – think

Use a point light source to project △ABC onto the curtain wall parallel to it to get △A′B′C′

Change the position of point light source O. What do you find?

① △ABC ∽△A′B′C′

②The lines connecting corresponding points intersect at one point

③Corresponding sides are parallel to each other

Cooperation and exchange

1. In the picture above, the two polygons are not only similar, but the lines connecting the corresponding vertices intersect at one point. The two figures like this are called similitude shapes, and this point is called the simulancy center. (Corresponding sides are parallel to each other)

(1) Are ΔABC and ΔA1B1C1 and ΔABC and ΔA2B2C2 similar respectively? Why?

(2) What are the other characteristics of the positions of ΔABC and ΔA1B1C1 and ΔABC and ΔA2B2C2?

2. What are the properties of position-like shapes?:

(1) Two similar shapes must be similar shapes;

(2) The straight lines corresponding to the vertices all pass through the same point;

(3) The ratio of the distances between corresponding vertices to the similarity center is equal to the similarity ratio.

Similar graphic features:

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.

3.⑴As shown in the figure, given A(2,0), write the coordinates of B and C.

⑵ Multiply the abscissa and ordinate coordinates of A, B, and C by 2. The resulting points form △A′B′C′. Write the coordinates of A′, B′, and C′, and draw △A′B′C′.

⑶ Taking O as the center of the position, according to the scale of 2:1, enlarge △ABC to △DEF

Drawing and Thinking

(1) Take point P as the similarity center and enlarge the figure according to the similarity ratio 2:1 to obtain Figure 1;

(2) Taking point Q as the similarity center, reduce the figure according to the similarity ratio of 1:2 to obtain Figure 2.

The similarity ratio between Figure 1 and Figure 2 is (), and the ratio of areas is ().

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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: 2024-10-02

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

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