"Regular Polygons and Circles" PPT courseware

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"Regular Polygons and Circles" PPT courseware

Regular polygon: A polygon with all equal sides and equal angles is called a regular polygon.

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

Think about it:

Is a rhombus a regular polygon? Is a rectangle a regular polygon? Why?

Arcs are equal

Chords are equal (the sides of polygons are equal)

The angles of circles are equal (the angles of polygons are equal)

Prove: ∵AB=BC=CD=DE=EA

∴AB=BC=CD=DE=EA

∵BCE=CDA=3AB

∴∠1=∠2

Similarly ∠2=∠3=∠4=∠5

And ∵ vertices A, B, C, D, and E are all on ⊙O,

∴Pentagon ABCDE is the inscribed pentagon of ⊙O.

Center of a regular polygon: The center of the circumcircle of a regular polygon.

Radius of regular polygon: Radius of circumscribed circle

Central angle of a regular polygon: The central angle subtended by each side of the regular polygon.

The distance between the sides of a regular polygon: the distance from the center to one side of the regular polygon.

Quick answer questions:

1. O is the center of positive △ABC, and it is the center of the circumcircle and inscribed circle of △ABC.

2. OB is called the radius of positive △ABC, which is the radius of the circumcircle of positive △ABC.

3. OD is called the edge-center distance of positive △ABC, which is the radius of the inscribed circle of positive △ABC.

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

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

4. Properties of regular polygons:

1. All sides of a regular polygon are equal

2. All angles of a regular polygon are equal

3. Regular polygons are all axis-symmetric figures. A regular n-gon has n axes of symmetry, and each axis of symmetry passes through the center of the n-gon.

4. Whether it is a regular polygon with an even number of sides or a centrally symmetrical figure, its center is the center of symmetry.

How to draw a regular polygon

1. Use a protractor to bisect the circle

2. Use ruler and compass to draw equal circles

(1) Rule and compass drawing of regular square and regular octagon

(2) Rule and compass drawing of regular six, regular three and regular dodecagon

summary:

1. What kind of polygon is a regular polygon?

Can you give an example?

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

2. How to determine whether a polygon is a regular polygon?

According to the first theorem of the relationship between regular polygons and circles

Compliance testing:

1. Judgment question.

① A polygon with all sides equal is a regular polygon. ( )

②A circle has one and only one inscribed regular polygon. ( )

2. Proof question.

Prove: The polygon obtained by connecting the midpoints of each side of a regular hexagon in sequence is a regular hexagon.

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"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: 2024-10-05

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

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