"Regular Polygons and Circles" PPT

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"Regular Polygons and Circles" PPT

Part One: Introduction to the new lesson

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?

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 turn to obtain the regular pentagon ABCDE.

∵ Arc AB = Arc BC = Arc CD = Arc DE = Arc EA

∴AB=BC=CD=DE=EA,

arc BCE = arc CDA = 3 arc AB

∴ ∠A=∠B.

In the same way ∠B=∠C=∠D=∠E.

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

∴ Pentagon ABCD is the inscribed regular pentagon of ⊙O, and ⊙O is the circumscribed circle of pentagon ABCD.

Regular polygons and circles PPT, part 2: 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.

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.

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 one side of the regular polygon is called the edge-center distance of the regular polygon.

Regular polygons and circles PPT, the third part: analysis of examples

Example 1 Use a ruler and compass to construct a square inscribed in a circle.

Known: Figure 29-5-2, ⊙O.

Find the solution: Square ABCD is inscribed in ⊙O.

Method: (1) As shown in Figure 29-5-3, draw two mutually perpendicular diameters AC and BD.

(2) Connect AB, BC, CD, DA in sequence.

It can be seen from the drawing process that the four central angles are all 90°, so AB=BC=CD=DA.

Because AC and BD are both diameters, ∠ABC=∠BCD=∠CDA=∠DAB=90°.

That is, the quadrilateral ABCD is an inscribed square of ⊙O.

Regular Polygons and Circles PPT, Part 4: Selected Examples

1. If the radius of an equilateral triangle is 4, then its center-to-side distance is ____ and its side length is _____.

Focus: equilateral triangle, square, equilateral hexagon

2. There is a pavilion whose foundation is a regular hexagon with a radius of 4m (as shown in the picture). Find the perimeter and area of ​​the foundation.

If the perimeter of the regular polygon is l and the distance between the sides is r, then: S=____________.

Regular polygons and circles PPT, Part 5: How to draw a regular polygon?

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...

Regular polygons and circles PPT, part six: summary

1. Relevant concepts in regular polygons;

2. Symmetry of regular polygons;

3. Relevant calculations in regular polygons:

central angle = exterior angle = _____

Interior angle = ___________

Know the side length, radius, and edge-to-center distance.

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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: 2024-09-09

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