"Regular Polygons and Circles" PPT teaching courseware

"Regular Polygons and Circles" PPT teaching courseware

Part One: Regular Polygons

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

If a regular pentagon satisfies the condition:

AB=BC=CD=DE=EA

∠A=∠B=∠C=∠D=∠E

Regular n-gon:

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

Regular polygons and circles PPT, part 2: regular polygons and circles

Do you know what is the relationship between regular polygons and circles?

Given a circle, how can you make a regular polygon? Several equal arcs appear in sequence in a circle

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.

1: Let’s prove it by taking a circle inscribed in a regular pentagon as an example.

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

2. Is a polygon inscribed in a circle with all equal sides a regular polygon? What about a polygon inscribed in a circle with all equal angles? If so, explain why; if not, give a counterexample.

Answer: A polygon inscribed in a circle with equal sides is a regular polygon.

We call the center of the circumscribed circle of a regular polygon the center of the regular polygon.

The radius of the circumscribed circle is called the radius of the regular polygon.

The central angle subtended by each side of a regular polygon is called the central angle of the regular polygon.

The distance from the center to the regular polygon is called the edge-center distance of the regular polygon.

Regular polygons and circles PPT, part three content: 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.

Regular polygons and circles PPT, Part 4: Calculations related to regular polygons

[Demonstration Question 2] As shown in the figure, it is known that the perimeter of �O is equal to 6πcm, find the area of ​​the regular hexagon ABCDEF with its radius as the side length.

[Idea suggestion] Connect OD, OE, pass through point O and draw OH⊥DE in H. According to the perimeter formula, the radius can be found. OH is the height of the equilateral △DOE. Find OH according to the Pythagorean theorem and find △DOE. The area of ​​, you can get the area of ​​regular hexagon ABCDEF.

[Autonomous answer] Connect OD, OE, and pass the point O to make OH⊥DE in H, then EH=DH=DE,

Assume the radius of �O is R. From the question, we know that 2πR=6π,

∴R=3(cm).∵The side length of a regular hexagon is equal to the radius,

∴DE=3, in Rt△EOH, OE=3, EH=, obtained from the Pythagorean theorem,

OH=

∴The area of ​​regular hexagon ABCDEF is: (cm2).

【Think about it】

What is the quantitative relationship between the side length and radius of a regular hexagon? Why?

Tip: If they are equal, the central angle of a regular hexagon is 60°, and the sides and radius form an equilateral triangle.

Regular polygons and circles PPT, part five: conclusion summary

1. Definition and judgment: Prove that all sides of a polygon are equal and all angles are equal.

2. Determination of the relationship between a regular polygon and a circle: When a polygon is a polygon inscribed in a circle, it can be judged that the vertices of the polygon bisect the circle.

3. Angles related to regular n-sided polygons.

(1) Central angle: The number of each central angle is:

(2) Interior angles: The number of each interior angle is:

(3) Exterior angles: The measure of each exterior angle is:

Regular polygons and circles PPT, part six: reflection and summary, expansion and sublimation

1. What did you learn in this class?

2. What is the measure of an interior angle of a regular n-sided polygon? What about the central angle?

3. What is the relationship between the central angle and the size of the exterior angle of a regular polygon?

4. What are the properties of regular polygons?

5. What is the relationship between the radius, edge-to-center distance and side length of a regular n-sided polygon?

Keywords: Free download of mathematics PPT courseware for the second volume of the ninth grade of Hebei Education Edition, regular polygon and circle PPT download, .PPT format;

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"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...

"Regular Polygons and Circles" PPT:

"Regular Polygons and Circles" PPT Part One Content: New Lesson Explanation Question: What is the relationship between regular polygons and circles? Thinking: Divide ⊙O into 5 equal arcs, and connect these equal points in sequence. What figure will you get? Why? We use the incircle to connect positive five..