"Regular Polygons and Circles" PPT Courseware 2

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"Regular Polygons and Circles" PPT Courseware 2

think about it

equilateral triangle

Three sides are equal and three angles are equal (60°)

square

Four sides are equal and four angles are equal (90°)

regular polygon definition

A polygon with equal sides and equal angles is a regular polygon.

Regular n-gon: If a regular polygon has n sides, then the regular polygon is called a regular n-gon.

Explore new knowledge

Do you know the relationship between regular polygons and circles?

The relationship between regular polygons and circles is very close. As long as a circle is divided into equal arcs, the inscribed regular polygon of the circle can be made. This circle is the circumcircle of the regular polygon.

Let us prove this by taking a regular pentagon inscribed in a circle as an example.

As shown in the figure, divide ⊙O into 5 equal arcs, and connect the points in sequence to obtain the regular pentagon ABCDE.

∵AB=BC=CD=DE=EA

∴AB=BC=CD=DE=EA,

∴BCE=CDA=3AB

∴ ∠A=∠B.

In the same way ∠B=∠C=∠D=∠E.

And the vertices of ∵pentagon ABCDE are all on ⊙O,

∴ Pentagon ABCDE is an inscribed regular pentagon of ⊙O,

⊙O is the circumcircle of pentagon ABCDE.

concept learning

①We call the center of the circumcircle (inscribed circle) of a regular polygon the center of the regular polygon (i.e. point O)

②The radius of the circumscribed circle is called the radius of the regular polygon (i.e. OA)

③The central angle subtended by each side of a regular polygon is called the central angle of the regular polygon (i.e. ∠AOB)

④The distance from the center to one side of the regular polygon is called the edge-to-center distance of the regular polygon (the radius of the inscribed circle, or OM)

Synchronous practice

1. The center O of the circumcircle of square ABCD is called the center of square ABCD.

2. The radius OE of the inscribed circle of square ABCD is called the edge-center distance of square ABCD.

3. The central angle of regular hexagon ABCDEF in the figure is ∠AOB and its degree is 60 degrees.

4. What quantitative relationship did you find between the radius and side length of regular hexagon ABCDEF? Why?

Consolidation exercises

1. Each interior angle of a regular octagon is ______ degrees.

2. As shown in the figure, regular hexagon ABCDEF is inscribed in ⊙O, then the degree of ∠CFD is ( )

A. 60° B. 45° C. 30° D. 22.5°

3． If a regular polygon rotates 90° around its center to coincide with the original figure, then the regular polygon is ( )

A. equilateral triangle B. square

C. Regular pentagon D. Regular hexagon

4. It is known that the distance between the sides of a regular hexagon is √3, then its perimeter is _____.

Explore new knowledge

How to draw a regular polygon?

Question 1: Given that the radius of ⊙O is 2cm, find the inscribed equilateral triangle of the circle.

①Use a protractor to measure, so that ∠AOB=∠BOC=∠COA=120°.

② Use a protractor or a 30° triangle to measure, so that ∠BAO=∠CAO=30°.

Can you make regular hexagons, regular triangles, and regular dodecagons with a ruler and compass?

Cut six equal arcs on the circumference of the circle with the length of the radius, and connect the bisecting points in sequence to form a regular hexagon.

First make a regular hexagon, then you can make a regular triangle, a regular dodecagon, a regular 24-sided polygon...

Class summary

1. Properties of regular polygons:

1. All sides of a regular polygon are equal

2. All angles of a regular polygon are equal

2. Calculation of regular polygons:

3. How to draw regular polygons

1. Use a protractor to bisect the circle

2. Use ruler and compass to draw equal circles

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For more information about the "Regular Polygons and Circles" PPT courseware, please click on the "Regular Polygons and Circles" ppt tab.

"Regular Polygons and Circles" PPT teaching courseware:

"Regular Polygons and Circles" PPT teaching courseware Part One: Regular Polygons Regular polygons: A polygon with equal sides and equal angles is called a regular polygon. For example, the conditions satisfied by a regular pentagon are AB=BC=CD=DE=EA A=B=C=D=E Regular n-sided polygon: If a..

"Regular Polygons and Circles" PPT courseware download:

"Regular Polygons and Circles" PPT courseware download Part One: Question Exploration Question 1. What kind of figure is a regular polygon? A polygon with equal sides and equal angles is a regular polygon. Question 2. Can you name a few common regular polygons? Question 3: Exactly many...

"Regular Polygons and Circles" PPT download:

"Regular Polygons and Circles" PPT Download Part One Content: Main Points, Test Points Focus 1. The focus of this lesson is the calculation methods of regular polygons, the calculation methods of the perimeter and area of ​​circles and simple combined figures. 2. The definition of regular polygons: All sides are equal, so are all angles...

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Update Time: 2024-11-20

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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