"Exploring the Conditions for Similarity of Triangles" Similarity of Figures PPT Courseware 3

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"Exploring the Conditions for Similarity of Triangles" Similarity of Figures PPT Courseware 3

Review review:

Triangle similarity determination method

1. The definition of similar triangles can be used as a method to determine the similarity of triangles.

2. Two triangles with equal angles are similar.

3. Two triangles whose sides are proportional and have equal angles are similar.

Determination method three: If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar.

Simple statement: two triangles with three sides corresponding to proportions are similar.

Knowledge and skills

1. The lengths of the three sides of a triangle are 6 cm, 9 cm, and 7.5 cm respectively, and the lengths of the three sides of another triangle are 8 cm, 10 cm, and 12 cm respectively. Are these two triangles similar? Why?

2. As shown in the figure, are △ABC and △EFG similar? Why?

3． Which of the 6 triangles shown in the figure are similar? Why?

4. Connect three grid points on a piece of 8 × 8 grid paper to obtain a triangle. Among such triangles, find three pairs of similar triangles with different sizes, and indicate their similarity ratio.

Given △ABC and △A’B’C’, determine whether they are similar based on the following conditions.

(1)∠B＝∠B’＝75°, ∠C＝50°, ∠A’＝55°

(2) ∠A＝45°, AB=12cm, AC=15cm

∠A’=45°, A’B’=16cm, A’C’=20cm

(3) AB=12cm, BC=15cm, AC=24cm

A’B’=16cm, B’C’=20cm, A’C’=30cm

I want to make two triangular frames with the same shape. One frame has three side lengths of 3, 4, and 5, and the other frame has one side length of 6. How can I choose the materials to make the two triangles similar?

As shown in the figure, we know an isosceles triangle and a line segment. Draw a triangle with this line segment as a side to make it similar to the known isosceles triangle. How many different shapes of triangles can you draw?

As shown in the figure, in the square ABCD with side length 4a, BE=3CE, CF=DF.

(1) Try to explain: AE²=AF²+EF²

(2) Try to explain: △AEF∽△ADF

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For more information about the PPT courseware "Exploring the Similarity of Conditional Figures with Similar Triangles", please click the Similarity ppt tag of "Exploring the Similarity of Conditional Figures with Similar Triangles".

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 6:

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 6 Review the past and learn new things 1. What are similar triangles? Two triangles in which the angles are equal and the sides are proportional are called similar triangles. 2. What are congruent triangles? The triangles correspond to equals, and the three sides correspond to...

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 5:

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 5 Review and Thinking [Congruent Triangles] Two triangles with the same shape and equal size. That is: a triangle corresponds to three equal sides and two equal triangles are congruent. [Similar triangles] have the same shape and size..

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 4:

"Exploring the Conditions for Similarity of Triangles" Similar Figures PPT Courseware 4 Learning Objectives 1. Preliminarily master the conditions for determining the similarity of two triangles. 2. Experience the exploration process of two triangles with similar conditions to further develop students' exploration and communication abilities, as well as oral, hands-on,...

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Update Time: 2024-10-03

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

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