"Magnification and reduction of graphics" similar graphics PPT courseware 2

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"Magnification and reduction of graphics" similar graphics PPT courseware 2

Review and Thoughts

What are similar polygons?

What is the similarity ratio of similar polygons?

What are some ways to determine if two triangles are similar?

Do you still remember the method of using rubber bands to enlarge graphics on page 116 in the third section of this chapter?

Do you still remember how to make fish longer and fatter in the "Changing Fish" lesson last semester? How to enlarge the fish?

Can you use these methods to scale up and down a known polygon? Is there a better way?

Explore and think about special cases of similar graphics

The following set of pictures are graphics with the same shape. Take point A on picture ①. Does the line connecting it to the corresponding point B on another picture (such as picture ②) pass through the center of lens P? Change the picture Try other places, are there any similar conclusions?

Definition: If two figures are not only similar, but also the straight lines of each set of corresponding points pass through the same point, then such two figures are called similarity figures. This point is called the similarity center. The similarity ratio at this time is also called similarity. Compare.

Do it

Which shapes in the picture below are similar shapes? Which graphics are not bit-like graphics?

In the figure below, the two figures in (1) and (3) are similar figures, but the two figures in (2) are not similar figures.

Properties Properties of similitude figures: The ratio of the distances between any pair of corresponding points on the similitude figure to the similitude center is equal to the similitude ratio.

Open wisdom

Use the method of using a rubber band to enlarge the figure on P116 of Chapter 3 of this chapter , and you will find that the two figures before and after the enlargement are actually similar figures.

Can you use this method to enlarge a known polygon so that the bit ratios of the enlarged figure and the original figure are 3 and 4 respectively?

Do it

The three sides of △ABC can be reduced to 1/2 of their original size as follows:

As shown in the figure, take any point O, connect AO, BO, CO, and take their midpoints D, E, F;

The three sides of △DEF are 1/2 of the corresponding three sides of △ABC.

In fact, △ABC and △DEF are similar figures.

Do it

(1) If D, E, and F are taken on rays OA, OB, and OC respectively, so that OD=2OA, OE=2OB, and OF=2OC, what will be the result?

The result will be an enlarged △DEF, and the three sides of △DEF are twice the three sides of △ABC. That is, their bit-like ratio is 2:1.

(2) If we take points D, E, and F respectively on the rays AO, BO, and CO so that DO=OA, EO=OB, and FO=OC, then what will be the result?

The result will be a △DEF that is congruent with △ABC, that is, their similarity ratio is 1:1.

(3) If we take points D, E, and F respectively on the rays AO, BO, and CO so that DO=2OA, EO=2OB, and FO=2OC, what will be the result?

The result will be an enlarged △DEF, and the three sides of △DEF are twice the three sides of △ABC. That is, their bit-like ratio is 2:1.

think about it

Is the following statement correct? Why?

Take points D and E on the sides AB and AC of △ABC respectively, so that DE∥BC, then △ADE is the reduced figure of △ABC;

Take points D and E on the extension lines of sides AB and AC of △ABC respectively, so that DE∥BC, then △ADE is the enlarged figure of △ABC;

Take points D and E on the reverse extension lines of sides AB and AC of △ABC respectively, so that DE∥BC, then △ADE is the reduced figure of △ABC;

Practice in class

The vertex coordinates of △ABC are A(2,2), B(4,2), and C(6,4). Try to reduce △ABC so that the ratio of the reduced △DEF to the corresponding side of △ABC is 1: 2.

Reduce the horizontal and vertical coordinates of the three vertices to 1/2 of the original values ​​at the same time, and the resulting new triangle is a triangle that meets the conditions.

Summary and expansion

Similar graphics:

If two figures are not only similar, but also the straight lines of each set of corresponding vertices pass through the same point, then such 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. .

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

How to make positional images (enlargement and reduction; forward and inverted images).

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For more information about the PPT courseware "Enlarging and Reducing Similar Figures and Figures", please click the Enlargement and Reduction of Similar Figures PPT Figures ppt tab.

"Magnification and reduction of graphics" similar graphics PPT courseware 3:

"Amplification and Reduction of Figures" Similar Figures PPT Courseware 3 Learning Objectives 1. Understand the similarity figures and related concepts, and understand that the ratio of the distance between any pair of corresponding points on the similarity figures is equal to the similarity ratio. 2. Be able to Use the method of positioning a figure to place a figure...

"Magnification and reduction of graphics" similar graphics PPT courseware:

Review and Reflection of Similar Figures PPT Courseware "Enlarging and Reducing Figures" What are similar polygons?

What is the similarity ratio of similar polygons? What are some ways to determine if two triangles are similar? Do you still remember the use of rubber bands to enlarge graphics on page 104 of the third section of this chapter?

"Magnification and reduction of graphics" Transformation and position determination of graphics PPT courseware 3:

"Enlarging and Reducing Graphics" Transformation and Position Determination of Graphics PPT Courseware 3 These three sets of pictures have the same shape but different sizes. Like this: the shape is the same, but the figure becomes larger, which is called enlargement of the figure. The shape is the same, but the figure becomes smaller, which is called the reduction of the figure. The left picture is long (..

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Update Time: 2024-09-07

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