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Authoritative PPT Summary
"Side Area of a Cone" Circle PPT Courseware 3
teaching objectives
knowledge and abilities
Enable students to understand the concept of regular polygons and initially master the first theorem of the relationship between regular polygons and circles.
Through teaching the definition of regular polygons, students can develop their abilities of induction, observation, reasoning, and transfer.
Process and Method
Through review, students can improve their ability to summarize and systematize knowledge.
Improve students' ability to comprehensively analyze and solve problems through proofs and drawings.
Cultivate students' divergent thinking ability through training with multiple solutions to one question.
The relationship between regular polygons and circles is very close. By dividing a circle into equal arcs, you can create an inscribed regular polygon of the circle. This circle is the circumcircle of the regular polygon.
Theorem Proof
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 regular pentagon of ⊙O.
⊙O is the circumcircle of pentagon ABCDE.
Related concepts in regular polygons and circumscribed circles
Center: The center of the circumscribed circle of a regular polygon.
The radius of a regular polygon: the radius of the 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.
Practice in class
1. The measure of an interior angle of a regular n-sided polygon is ____________; the central angle is ___________; the relationship between the central angle and the exterior angle of a regular polygon is _____________.
2. O is the center of positive △ABC, and it is the center of the ________ circle and ________ circle of △ABC.
3. OB is called the ________ of positive △ABC, and it is the radius of the ________ circle of positive △ABC.
4. OD is called the ________ of positive △ABC, and it is the radius of the ________ circle of positive △ABC.
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