"Exploring the Conditions for Similarity of Triangles" Similarity of Figures PPT Courseware 4

Description

"Exploring the Conditions for Similarity of Triangles" Similarity of Figures PPT Courseware 4

The concept of golden section

Divide a line segment AB into two unequal parts, so that the ratio of the shorter line segment CB to the longer line segment AC is equal to the ratio of AC to the original line segment AB, that is, CB/AC=AC/AB

Then line segment AB is said to be golden sectioned by point C. Point C is called the golden section point of line segment AB. The ratio of the longer line segment AC to the original line segment AB is called the golden ratio.

mathematical understanding

1. As shown in the figure, a string AB = 80 cm on the musical instrument, the two endpoints A and B are fixed on the instrument board, the support point C is the golden section point close to point B, and the support point D is the golden section point close to point A ． Try to determine the distance from support point C to end point B and the distance from support point D to end point A.

The golden section point H of a known line segment AB can also be drawn using the method shown in Figure 3-22:

1. Construct a square ABCD on AB.

2. Take the midpoint E of AD and connect EB.

3． Extend DA to F so that EF = EB.

4. Construct a square AFGH with the line segment AF as a side.

Point H is the golden section point of AB.

Can you explain the rationale for this approach?

Class summary

What is the golden section? What is the golden ratio?

How many golden section points does a line segment have?

How to use a ruler and compass to create the golden section and golden rectangle of a line segment?

How to explain that a point is the golden section point of a line segment?

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For more information about the PPT courseware "Exploring the Similarity of Conditional Figures with Similar Triangles", please click the Similarity ppt tag of "Exploring the Similarity of Conditional Figures with Similar Triangles".

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Update Time: 2024-10-04

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

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