"Application of the Pythagorean Theorem" PPT download of the Pythagorean Theorem

"Application of the Pythagorean Theorem" PPT download of the Pythagorean Theorem

Part One: Learning Objectives

1. Learn to use the Pythagorean theorem to find the shortest distance between two points in a three-dimensional figure. (emphasis)

2. Be able to use the Pythagorean Theorem to solve problems in real life. (Key points, difficulties)

PPT on the application of the Pythagorean Theorem, part 2: teaching new courses

The shortest distance between two points in a solid figure

Question: On a cylindrical stone bench, if Xiao Ming leaves a little food at place B while eating, and an ant at place A happens to capture this information, so it wants to crawl from place A to place B, what do you think? Think about it, how do ants get closest?

If it is known that the height of the cylinder is 12 cm, the radius of the base is 3 cm, and π is 3, then:

[Method Summary] To find the shortest distance between two points in a three-dimensional figure, generally expand the three-dimensional figure into a plane figure, connect the two points, and determine the shortest route based on the shortest line segment between the two points.

Analysis of classic examples

Example 1 There is a cylindrical oil tank. It is necessary to build a ladder around the oil tank at point A, just above point A at point B. How many meters is the shortest length of the ladder? (It is known that the bottom radius of the oil tank is 2 m. The height AB is 5 m, and π is 3)

Solution: The expansion diagram of the oil tank is as shown in the figure, then AB' is the shortest distance of the ladder.

∵AA'=2×3×2=12, A'B'=5,

∴AB'=13. That is, the shortest ladder needs to be 13 meters.

Variation 1: When the little ant climbed to point E, which is 3cm away from the upper bottom, Xiao Ming’s hand holding the drink bottle shook, and the drop of sweet drink slid along the outer wall of the bottle to point F, which was 3cm away from the lower bottom. What is the shortest distance for the ant to reach point F? (π takes 3)

Variation 2: Seeing the excitement of the little ant finally drinking the drink, Xiao Ming suddenly had an idea. He took out the milk carton, placed the little ant at point A, and put some ham at point B. Intestine, can you help the little ant find the shortest way to complete the task?

Practical applications of the Pythagorean Theorem

Question: Uncle Li wanted to check whether the sides AD and BC on the front of the sculpture base are perpendicular to the bottom side AB, but he only brought a tape measure with him.

(1) Can you find a way to complete the task for him?

(2) The length AD is measured to be 30 cm, the length AB is 40 cm, and the length BD is 50 cm. Is side AD perpendicular to side AB?

(3) If you only have a scale with a length of 20 cm, is there a way to check whether side AD is perpendicular to side AB?

PPT on the application of the Pythagorean Theorem, part 3: practice in class

1. The picture shows a piece of paper with a right triangle. The two right-angled sides AC=6 cm and BC=8 cm. Fold △ABC so that point B coincides with point A. The fold is DE, and the length of BE is ( )

A.4 cm B.5 cm C.6 cm D.10 cm

2. There is a cylindrical oil drum with a height of 1.5 m and a radius of 1 m. There is a small hole near the edge. An iron rod is inserted through the hole. It is known that the part of the iron rod outside the oil drum is 0.5 m. What is the question? How long is an iron rod?

3. A 25m long ladder AB is leaning against a vertical wall AO. At this time, the distance between AO is 24m. If the top A of the ladder slides down 4m along the wall, does the bottom B of the ladder also move outward 4m?

4. An interesting question is recorded in the ancient Chinese mathematics work "Nine Chapters of Arithmetic". The meaning of this question is: There is a pool, the water surface is a square with a side length of 10 feet, and there is a new reed in the center of the pool. It is 1 foot above the water surface. If this reed is pulled vertically towards the shore, its top just reaches the water surface of the shore. What are the depth of the pool and the length of the reed?

PPT on the application of the Pythagorean Theorem, part 4: Class summary

The shortest distance between two points in a solid figure

Practical applications of the Pythagorean Theorem

Keywords: Beijing Normal University Edition eighth grade mathematics PPT courseware free download, application of Pythagorean Theorem PPT download, Pythagorean Theorem PPT download, .PPT format;

For more information about the "Pythagorean Theorem Application of the Pythagorean Theorem" PPT courseware, please click the Pythagorean Theorem PPT Application of the Pythagorean Theorem PPT tab.

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