"Properties of Similar Triangles" Similarity PPT courseware for graphics

Description

"Properties of Similar Triangles" Similarity PPT courseware for graphics

problem situation

When comparing the triangle seen under a 10x magnifying glass with the original triangle, which side lengths, perimeters, areas, and angles of the triangle are magnified 10x?

The three main line segments in a triangle:

height line, angle bisector, midline

What is the relationship between the similarity ratio of similar triangles and the height ratio of the corresponding sides?

For example: ΔABC∽ΔA/B/C/, AD BC in D,

A/D/B/C/YuD/,

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

②The ratio of the corresponding angle bisectors and the ratio of the midlines of similar triangles are equal to the similarity ratio.

When comparing the triangle seen under a 10x magnifying glass with the original triangle, which side lengths, perimeters, areas, and angles of the triangle are magnified 10 times?

Answer: The side lengths and perimeter of a triangle are magnified 10 times.

The area of ​​the triangle is enlarged 100 times.

The angles of the triangle remain unchanged in size.

1. Judgment question:

(1) If all sides of a triangle are expanded to 5 times their original size at the same time, then its perimeter will also be expanded to 5 times its original size. (√)

(2) If the area of ​​a triangle is expanded to 9 times its original size, then its three sides will also be expanded to 9 times its original size. (×)

2. As shown in the figure, △ABC∽△A�B�C�, their circumferences are 60cm and 72cm respectively, and AB=15cm, B�C� =24cm,

Find the lengths of BC, AC, A�B�, and A�C�.

Properties of similar triangles:

(1) The ratio of the midline, altitude, and 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.

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

Class Quiz:

(1) It is known that the similarity ratio between ΔABC and ΔA/B/C/ is 2:3, then the perimeter ratio is _______, the ratio of the midlines on the corresponding sides is _______, and the area ratio is _______.

(2) It is known that ΔABC∽ΔA/B/C/, and the ratio of areas is 9:4, then the ratio of perimeter is _______, the similarity ratio is _______, and the ratio of the height lines on the corresponding sides is _______.

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For more information about the PPT courseware "Properties of Similar Triangles and Similarity of Figures", please click the Similarity ppt tag of "Properties of Similar Triangles ppt Figures".

"Properties of Similar Triangles" PPT Courseware 3:

"Properties of Similar Triangles" PPT Courseware 3 Situation Introduction: Known: ABC∽A'B'C', according to the definition of similarity, what conclusions do we have? Viewed from corresponding sides: __________________ Viewed from corresponding angles: __________________ Two triangles..

"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...

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Update Time: 2024-10-04

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

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