"Pythagorean Theorem" PPT courseware 7

Description

"Pythagorean Theorem" PPT courseware 7

learning target

Understand the discovery process of the Pythagorean Theorem, master the content of the Pythagorean Theorem, and be able to use the area method to prove the Pythagorean Theorem.

Be able to use the Pythagorean Theorem to perform simple calculations, develop a rigorous attitude toward mathematical learning, and appreciate the application value of the Pythagorean Theorem.

Independent exploration and understanding of new knowledge

1. In Figure 1(2), Δ ABC is a right triangle, ∠ ACB = 90°.

(1) If each small square grid is a square with side length 1, then what are the lengths of the three sides AC, BC, and AB of Rt ΔABC? What are the areas of the three squares with AC, BC, and AB as sides? How many are each? What is the equivalence relationship between these areas?

(2) If the lengths of the three sides of this right triangle are a, b, and c respectively, how can we use a, b, c to express the relationship between the areas of the three squares in the picture?

2. Figure 2 (1) is a floor paved with square tiles of two colors of the same size.

(1) What is the equivalence relationship between the areas of the three squares marked with white boxes in Figure 2(1)?

(2) According to Figure 2 (2), can you tell how the equivalence relationship between the areas of squares reflects the relationship between the three sides of Rt ΔABC? Write it out.

Verify experiments and discover patterns

1. Take out the four prepared congruent right triangles (let the two right-angled sides of the right triangle be a, b, and the hypotenuse c);

2. Can you use these four right triangles to form a square? Give it a try

3. Does the square you put together contain a regular shape with hypotenuse c?

4. Can you explain a2+b2=c2 based on the picture you spelled out?

(Pythagorean syndrome)

As shown in the picture, there are 8 pieces of the same right-angled triangle paper. Let the right-angled sides be a and b respectively, and the hypotenuse be c; there are two squares with side lengths (a+b). Now I place 4 of the right-angled triangle pieces of paper in the first picture; I place the other 4 right-angled triangle pieces of paper in the second picture. Ask the students to observe what is the relationship between the areas of the three small squares I, II and III in the two figures? Tell us about your findings.

Pythagorean theorem (gou-gu theorem)

If the two right-angled sides of a right triangle are a and b, and 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.

Our country has known this theorem for more than 3,000 years. People call the upper part of an arm bent at a right angle a "hook" and the lower part a "strand". Ancient Chinese scholars call the shorter right-angled side of a right-angled triangle It is called "hook", the longer right-angled side is called "strand", and the hypotenuse is called "string". Therefore, this theorem is called the Pythagorean theorem.

1. Fill in the blanks

1) In a right triangle, the two right-angled sides are a and b, and the hypotenuse is c, then c2=____

2) In RT△ABC, ∠C=90°,

⑴If a=4,b=3, then c=____

⑵If c=13, b=5, then a=____

3) In a right triangle, if two sides are 3 and 4, then the other side is _________

⑵As shown in the figure, in RT△ABC, ∠C=90°,

∠B=45°, AC=1, then AB=( )

A2, B1, C√2, D√3

Example study

Example 1 As shown in Figure 5-2, a steel wire rope is pulled from point A at the top of telephone pole OA and fixed to point B on the ground. What is the length of this wire rope?

Analysis: Connect OB, OB is perpendicular to OA, and a right-angled triangle is obtained. In this right-angled triangle, if the two right-angled sides are known to find the hypotenuse, the Pythagorean theorem should be used.

Solution As shown in the figure, in Rt△AOB, ∠O=90°,

AO=8 meters, BO=6 meters,

From the Pythagorean theorem, we get

AB2=AO2+BO2

=82+62=100

So AB=√100 =10

Therefore, the length of the wire rope is 100 meters.

Talk about your gains!

1. What did you gain from this class?

2. What should we pay attention to when understanding the "Pythagorean Theorem"?

3. Do you think the "Pythagorean Theorem" is useful?

Teacher's message

We must develop the habit of using mathematical thinking to interpret the world.

Only through constant thinking can new discoveries be made; only through quantitative changes can there be qualitative progress.

In fact, mathematics is everywhere in our lives. As long as you are a thoughtful person, you will definitely find that there is a lot of knowledge like "Pythagorean Theorem" waiting for us to explore and discover around us and in front of our eyes. …

Homework snacks:

1. Complete textbook exercises 1, 2, and 3 (required)

2. Small experiment after class: As shown in the figure, three semicircles are made with the three sides of a right triangle as diameters. What is the relationship between the areas of these three semicircles? Why? (Must do)

3. Make a wonderful Pythagorean tree (optional)

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For more information about the "Pythagorean Theorem" PPT courseware, please click on the Pythagorean Theorem ppt tab.

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Update Time: 2024-10-12

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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