"Measuring Height with Similar Triangles" similar PPT courseware for graphics

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"Measuring Height with Similar Triangles" similar PPT courseware for graphics

Method 1: Use the shadows in the sun

∵The sun’s rays are parallel

∴AB∥DE

And B, C, E, F are on a straight line

∴ ∠ABC= ∠DEF

∵The person and the flagpole are perpendicular to the ground

∴∠ACB= ∠DFE

∴△ABC∽△DEF

Because the classmate’s height AC, her shadow length BC and the flagpole’s shadow length EF at the same time can all be measured, the height of the flagpole DF can be calculated by substituting the measurement data.

Take advantage of the shadows in the sun.

Measurement data: height AC, shadow length BC, flagpole shadow length EF.

Find similarities: △ABC∽△DEF.

Find the ratio: DF:AC=EF:BC

Method 2: Use benchmarks

Operation method: 1. Stand a benchmark pole with a known height on the ground between the observer and the flagpole;

2. The observer adjusts his or her position back and forth until the top of the flagpole, the top of the benchmark pole and the eyes are exactly in the same straight line;

3. Measure the distance between her feet and the bottom of the flagpole and the bottom of the benchmark. The height of the student's eyes to the ground can be used to calculate the height of the flagpole;

Measurement: AB EF AM AN

The structure is similar: △AME∽△ANC.

Find the ratio: AM: AN=EM: CN

Method 3. Use mirror reflection

Operation method: 1. Select a student as the observer, place a mirror flat on the ground between her and the flagpole, and fix the position of the mirror;

2. The observer looks at the mirror and adjusts his position back and forth so that he can see the top of the flagpole through the mirror.

3. Measure the distance between her feet and the mirror and the distance between the bottom of the flagpole and the mirror to find the height of the flagpole.

Class summary

In real life, we face the inability to directly measure the length, height and width of objects. You can build similar triangle models, convert them into mathematical problems, convert the difficult-to-measure sides into problems of measuring their corresponding sides, and then use the proportion of the corresponding sides to achieve the purpose of solution.

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"Measuring Height with Similar Triangles" Similar PPT courseware for graphics 2:

"Measuring Height with Similar Triangles" Similarity PPT Courseware 2 of Figures Think about how students can use the knowledge of similar triangles to measure the height of a flagpole (or street lamp, tree or chimney)? Key points of the method Application method 1: The sunlight can be approximated Seen as parallel rays,...

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Update Time: 2024-10-03

This template belongs to Mathematics courseware Beijing Normal University Ninth Grade First Volume Mathematics industry PPT template

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