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

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

1. Two polygons whose angles are equal and whose sides are proportional are called similar polygons.

2. The ratio of corresponding sides of similar polygons is called the similarity ratio.

3. Corresponding angles of similar polygons are equal and corresponding sides are proportional.

Concept of similar triangles: Two triangles whose angles are equal and whose sides are proportional are called similar triangles.

△ABC is similar to △A1B1C1

Expressed as: △ABC∽△ A1B1C1

Pronounced as: △ABC is similar to △ A1B1C1

Note: When writing that two triangles are similar, the letters representing the corresponding vertices should be written in the corresponding positions.

think about it

If two triangles have only one angle that is equal, are they necessarily similar? What if there are two angles that are equal?

Please draw a triangle according to the following conditions,

Work in pairs, one person draws △ABC, the other person draws △A1B1C1

(1) Let ∠A= ∠A1 ＝45 ° ∠B= ∠B1 ＝30 °

(2) Let ∠A= ∠A1 ＝60 ° ∠B= ∠B1 ＝45 °

practise:

1. In ΔABC and ΔDEF, ∠A=40°, ∠B=80°, ∠E=80°, ∠F=60°. ΔABC vs. ΔDEF ("similar" or "dissimilar").

2. Determine whether the following statements are correct? and explain the reasons.

(1) Two right triangles with equal acute angles are similar. ( )

(2) Two isosceles triangles with equal vertex angles are similar. ( )

(3) Two isosceles triangles with an angle of 100° are similar. ( )

(4) Two isosceles triangles with an angle of 70° are similar. ( )

3. As shown in the figure, D and E are points on sides AB and AC of △ABC respectively, DE∥BC

⑴What are the equal angles in the picture?

⑵ Find similar triangles in the picture and explain the reasons.

⑶Write the three proportional line segments.

Class summary

1. Concept of similar triangles:

Two triangles whose angles are equal and whose sides are proportional are called similar triangles.

△ABC is similar to △A1B1C1

Expressed as: △ABC∽△ A1B1C1

Pronounced as: △ABC is similar to △ A1B1C1

Note: When writing that two triangles are similar, the letters representing the corresponding vertices should be written in the corresponding positions.

2. Triangle similarity determination method 1

If two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

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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".

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Update Time: 2024-09-27

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

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