"Properties of Similar Triangles" PPT Courseware 3

Description

"Properties of Similar Triangles" PPT Courseware 3

Situation introduction:

Given: ΔABC∽ΔA'B'C', based on similar definitions, what conclusions do we have?

Viewed from the corresponding side: ____________________

Viewed from corresponding angles: ____________________

Two triangles are similar. In addition to corresponding sides being proportional and corresponding angles being equal, what other conclusions can we draw?

For example: △ABC and △A′B′C′ are similar triangles, the similarity ratio is k, where AD and A′D′ are the heights of sides BC and B′C′ respectively, then there is what relationship?

From this it can be concluded that the ratio of the corresponding heights of similar triangles is equal to the similarity ratio

Change 1: What if the corresponding height is changed to the center line on the corresponding side?

Change 2: What if the corresponding height is changed to the angle bisector of the corresponding angle?

Let’s carefully observe the following set of graphics:

In the figure (1), (2), and (3) are equilateral triangles with side lengths 1, 2, and 3 respectively. Are they all similar? Why?

The similarity ratio between (2) and (1) =____________________,

The circumference ratio of (2) to (1) = ______________;

The area ratio of (2) to (1) =______________;

The similarity ratio between (3) and (1) =____________________,

The ratio of the circumference of (3) to (1) = ______________.

The area ratio of (3) to (1) =____________________.

Let me give it a try:

1. The ratio of the corresponding sides of similar triangles is 3:5, then the similarity ratio is ___________, the ratio of the angle bisectors of the corresponding angles is ______, the ratio of the perimeters is _____, and the ratio of the areas is _____.

Change: The ratio of corresponding sides of similar triangles is 9:8?

The ratio of corresponding sides of similar triangles is 0.5?

2. The ratio of the corresponding heights of two similar triangles is 2:5, then the ratio of the corresponding angle bisectors is ____, and the ratio of the perimeters is ___.

3. The ratio of the corresponding midlines of two similar triangles is 1:4, then the corresponding height ratio is ______ and the area ratio is ______.

Show style:

1. The ratio of the perimeter of a small triangle cut by the line segment connecting the midpoints of both sides of the triangle to the original triangle is equal to ______, and the ratio of the area is equal to _______.

2. The corresponding midline lengths of two similar triangles are 6cm and 18cm respectively. If the perimeter of the larger triangle is 42cm² and the area is 12cm², then the perimeter of the smaller triangle is ________cm and the area is ____.

3. As shown in the figure, there are △A1B1C1 and △A2B2C2 on the square grid. Are these two triangles similar? If they are similar, find the area ratio of △A1B1C1 and △A2B2C2.

4. As shown in the figure, points D and E are points on sides AB and AC of △ABC respectively, and DE∥BC, BD=2AD, then the perimeter of △ADE �The perimeter of △ABC=______.

Class summary

What properties will we learn about similar triangles today?

1. The ratio of corresponding heights of similar triangles is equal to the similarity ratio.

The ratio of the corresponding midlines of similar triangles is equal to the similarity ratio,

The ratio of the corresponding angle bisectors of similar triangles is equal to the similarity ratio.

2. The ratio of the perimeters of similar triangles is equal to the similarity ratio.

The ratio of the areas of similar triangles is equal to the square of the similarity ratio.

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For more information about the "Properties of Similar Triangles" PPT courseware, please click on the "Properties of Similar Triangles" ppt tab.

"Properties of Similar Triangles" PPT Courseware 2:

"Properties of Similar Triangles" PPT Courseware 2 1. The ratios of the corresponding heights, the ratios of the corresponding midlines, and the ratios of the corresponding angle bisectors of similar triangles are all equal to ________. 2. The ratio of the perimeters of similar triangles is _________. 3. The ratio of the areas of similar triangles is equal to______..

"Properties of Similar Triangles" PPT courseware:

"Properties of Similar Triangles" PPT courseware Learning Objectives 1. Master the properties theorem of similar triangles. 2. Master the comprehensive application of the determination theorem and property theorem of similar triangles to solve problems. 3. Further experience the learning idea of ​​analogy. 4. Through similar properties...

"Properties of Similar Triangles" Similar PPT Courseware of Figures 3:

"Properties of Similar Triangles" Similarity of Figures PPT Courseware 3 Fill in the blanks: The _______ of two similar triangles are equal and _______ are proportional. The ratio of the corresponding heights of similar triangles, the ratio of the corresponding midlines of similar triangles, and the ratio of the corresponding angle bisectors of similar triangles are all equal to...

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Update Time: 2024-06-11

This template belongs to Mathematics courseware Hebei Education Edition Ninth Grade Mathematics Volume 1 industry PPT template

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