"Measuring the Height of the Flagpole" Similar Graphics PPT Courseware 3

Description

"Measuring the Height of the Flagpole" Similar Graphics PPT Courseware 3

learning target

1. By measuring the height of the flagpole, students can comprehensively use the conditions and properties of similar triangles to solve problems, develop students' awareness of mathematical applications, and deepen students' understanding of similar triangles.

2. During group cooperation activities and whole-class communication, students can further accumulate mathematical experience and successful experience, and enhance students' self-confidence in learning mathematics.

Knowledge explanation

How to use the knowledge of similar triangles to measure the height of a flagpole (or streetlight, tree, or chimney)?

Method 1: Use the shadows in the sun

1.Are the two triangles in the picture similar? Why?

2. Use the shadow under the sun to measure the height of the flagpole. What data do you need to measure to calculate the height?

Method 2: Use benchmarks

1. Discussion: How to convert the figure into similar triangles by adding auxiliary lines?

2. Use a benchmark to measure the height of the flagpole. What data need to be measured to calculate the height?

Track training

As shown in the figure, there is a mirror E placed flat on the ground 18 meters away from AB. When a person steps back to D, which is 2.1 meters away from the mirror, he can see the top of the tree in the mirror. If the human eye is 1.4 meters away from the ground, find the height of the tree.

Solution: Let the height of the tree be x meters

Because △ABE∽△CDE

So AB/CD=BE/DE

x/1.4=18/2.1

x=12,

Answer: The tree is 12 meters high

Practice in class

1. (2010·Neijiang High School Entrance Examination) As shown in the picture, in order to measure the height of a certain tree, Xiao Ming used a 2m long bamboo pole as a measuring tool and moved the bamboo pole so that the end points of the shadows of the bamboo pole and the top of the tree fell exactly at the same point on the ground. , at this time, the bamboo pole is 6m away from this point and 15m away from the tree, then the height of the tree is _______m.

2. (2010 Gansu High School Entrance Examination) At the same moment, the shadow length of a 1.6-meter-tall Xiaoqiang in the sun is 0.8 meters, and the shadow length of a big tree is 4.8 meters. Then the height of the tree is ______ meters.

[Analysis] Suppose the height of this tree is x meters, then 1.6:x=0.8:4.8,

The solution is x=9.6, which means the height of the tree is 9.6 meters.

Answer: 9.6

3. The distance between the bottoms of street lamps A and B is 30 meters. One night, when Xiaohua walked 5 meters away from the bottom of street lamp B, he found that the top of his figure was just touching the bottom of street lamp B. It is known that Xiaohua's height is 1.5 meters, then the height of street lamp A is ______ meters.

Summary of this lesson

Through the study of this class, we need to master:

1. Use the shadow in the sun, the reflection of the benchmark and the mirror to measure the height of the flagpole;

2. When the measured object cannot be measured directly, we often use the properties of similar triangles to measure the height of the object;

3. Using these three measurement methods, the measurement results are allowed to have errors.

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For more information about the PPT courseware "Measure the Height of the Flagpole with Similar Figures", please click on the Measuring the Height of the Flagpole ppt with Similar Figures ppt tag.

"Measuring the Height of the Flagpole" Similar Graphics PPT Courseware 2:

"Measuring the height of the flagpole" Similar graphics PPT courseware 2 Expand your thinking How can students use the knowledge of similar triangles to measure the height of the flagpole (or street lamp or tree or chimney)? Key points of the method Application method 1: Sunlight can be viewed as parallel approximately Light, when calculating...

"Measuring the height of the flagpole" similar graphics PPT courseware:

"Measuring the Height of the Flagpole" Similar Figures PPT Courseware Activity 1 Read textbook page P141 and complete the following questions: 1. Are the two triangles in Figure 4-20 similar? Why? 2. Use the shadow in the sun to measure the height of the flagpole. What needs to be measured? Do you need data to calculate height? ..

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Update Time: 2024-10-14

This template belongs to Mathematics courseware Beijing Normal University eighth grade mathematics volume 2 industry PPT template

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