"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 3

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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 3

1. Situation introduction

The 2002 World Congress of Mathematicians was held in Beijing, my country. The following picture is the logo of this Congress of Mathematicians:

The pattern in the center of the monogram is Zhao Shuang's string diagram, which is related to the "Pythagorean Theorem". Mathematicians once suggested using the "Pythagorean Theorem" diagram as a signal to contact "aliens".

2. Explore and discover the Pythagorean Theorem

Research activity one:

Observe the floor tile diagram below:

Do you see any relationship between the areas of the three squares in the picture?

Conclusion 1 The sum of the areas of the small squares whose sides are the two right-angled sides of an isosceles right triangle is equal to the area of ​​the square whose sides are the hypotenuse.

Conclusion 2 The sum of the areas of the small squares with the two right-angled sides of the right triangle as the side length is equal to the area of ​​the square with the hypotenuse as the side length.

Pythagorean theorem

If the lengths of the two right-angled sides of a right triangle are a and b respectively, and the length of the hypotenuse is c, then a²+b²=c²

That is, the sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse.

Application in daily life:

Xiao Ming's mother bought a 29-inch (74 cm) TV. After Xiao Ming measured the TV screen, he found that the screen was only 58 cm long and 46 cm wide. He thought the salesperson must have made a mistake. Do you agree with him? ? Can you explain why this is?

4. Class Summary

1. What knowledge and thinking methods have we learned together in this class?

2. What is your experience with these contents? Please communicate with your peers.

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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 6:

"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 6 Read the textbook and answer the questions (1) Observe Figure 2-1. Square 1 contains ____ small squares, that is, its area is ____ unit area. The area of ​​square 2 is ____ unit area. The area of ​​square 3 is_..

"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 5:

"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 5 The specific method of independent exploration activities before class is: Ask each study group to find and understand as many methods as possible to verify the Pythagorean Theorem from the Internet or books. Analysis of the verification process. And appreciate the first type: to...

"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 4:

"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 4 Question Situation 1. In the last class, we have obtained the Pythagorean Theorem through exploration. What is the content of the Pythagorean Theorem? 2. How to verify the Pythagorean Theorem? According to incomplete statistics, there are more than 400 verification methods. You...

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Update Time: 2024-07-04

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