"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT (Lesson 2)

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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT (Lesson 2)

Part One: Learning Objectives

1. Learn to use several methods to verify the Pythagorean Theorem. (emphasis)

2. Be able to use the Pythagorean Theorem to solve simple problems. (main difficulty)

Exploring the Pythagorean Theorem PPT, part 2: teaching new lessons

Verification of the Pythagorean Theorem

Question: We learned about the Pythagorean Theorem in the last class. Do you still remember its content? So how to verify the Pythagorean Theorem?

According to incomplete statistics, there are more than 400 verification methods. Do you have your own method?

Verification method one: Pythagorean proof

The area of ​​the large square can be expressed as c2;

It can also be expressed as 4·1/2ab+(b- a)2.

Verification method two: Zhao Shuangxian diagram

The area of ​​the large square can be expressed as c2;

It can also be expressed as 4·1/2ab+(b- a)2.

A simple application of the Pythagorean Theorem

Example 1: Our investigator Xiao Wang was conducting reconnaissance 400m away from the east-west highway and found an enemy car speeding on the road. He quickly took out his infrared rangefinder and measured that the car was 400m away from him. After 10 seconds, the car He is 500m away. Can you help Xiao Wang calculate the speed of the enemy car?

Solution: According to the Pythagorean theorem, AB2=BC2+AC2,

That is 5002=BC2+4002,

Therefore, BC=300.

The enemy car traveled 300m in 10 seconds, then the distance it traveled in 1 hour is 300×6×60=108000 (m)

That is, it is traveling at a speed of 108km/h.

Example 2: As shown in the figure, there are two villages A and B on the same side of the highway. The distances from them to the straight line MN where the highway is located are AA1=2km, BB1=4km, and A1B1=8km. Now we want to locate A1 and B on the highway. Set an exit P between B1 so that the sum of the distances from villages A and B to P is the shortest. Find the sum of the shortest distances.

Exploring the Pythagorean Theorem PPT, Part 3: Practice in class

1. In a right triangle, the lengths of the three sides that meet the conditions can be _______. (Just write down a group)

[Analysis] The answer is not unique, as long as it satisfies the formula a2+b2=c2.

Answer: 3, 4, 5 (anything that meets the meaning of the question is acceptable)

2. As shown in the picture, Uncle Wang is going to build a vegetable greenhouse. The width of the greenhouse is 8m, the height is 6m, and the length is 20m. The slope of the greenhouse is covered with plastic film. Regardless of the thickness of the wall, the maximum area through which sunlight can penetrate is ________.

3. As shown in the picture, a flagpole was broken 9 m above the ground, and the top of the flagpole fell 12 m from the bottom of the flagpole. How high was the flagpole originally?

4. As shown in the picture, a certain residential area left an open space during the construction process (the quadrilateral ABCD in the picture). After measurement, in the quadrilateral ABCD, AB=3m, BC=4m, AD=13m, ∠B=∠ACD =90°． In order to beautify the environment, the community wants to lay lawn on the open space. It is known that the lawn costs 100 yuan per square meter. How many yuan will it cost to cover the open space?

5. As shown in the figure, fold side AD of rectangle ABCD so that point D falls at point F of side BC. If AB=8cm and BC=10cm, find the length of EC.

Exploring the Pythagorean Theorem PPT, Part 4: Class Summary

Verification of the Pythagorean Theorem

Simple application of the Pythagorean Theorem

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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT (Lesson 1):

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Update Time: 2024-07-10

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