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Category | Format | Size |
---|---|---|
Beijing Normal University Ninth Grade Mathematics Volume 2 | pptx | 6 MB |
Description
"Symmetry of Circles" Circle PPT Courseware 4
New course introduction
A circle is an axially symmetrical figure
The axis of symmetry is any straight line passing through the center of the circle
A circle is a centrally symmetrical figure
The center of symmetry is the center of the circle
Among the shapes we have learned, which ones are both axially symmetrical and centrally symmetrical?
Discuss
In equal circles, two students first make a central angle with the same degree!
In the same circle, draw two central angles of the same degree in your own circle!
In congruent or equal circles, equal central angles subtend equal arcs and subtend equal chords.
in conclusion
In congruent or equal circles,
If one set of quantities among two central angles, two arcs, two chords, and two chord-center distances are equal, then the other sets of quantities corresponding to them are equal!
Practice in class
1. (2011·Zhoushan High School Entrance Examination) In the figure, AB is the diameter of the semicircle, the radius OC⊥AB is at point O, AD bisects ∠CAB and intersects arc BC at point D. Connecting CD and OD, the following four conclusions are given: ①AC∥OD ; ②CE=OE; ③△ODE∽△ADO; ④CD2=CE·AB. The sequence number of the correct conclusion is.
[Analysis] Because OA=OD, bisecting ∠CAB by AD yields ∠OAD=∠DAC, so ∠CAD=∠OAD. So AC∥OD; bisecting ∠CAB from AD yields ∴∠AOD=∠DOC, and ∠CAD =∠ OAD, ∠ADC=45°, ∴∠COD=45°, ∠CDE=∠COD=45°, ∠DCE=∠OCD, ∴△DCE∽△OCD, ∴2CD2=CE·AB
Answer: ①④
2. (2010 Foshan High School Entrance Examination) As shown in the figure, the straight line and the two concentric circles intersect at each point in the figure, then the correct answer is ( )
A. The relationship between MP and RN is uncertain B.MP=RN C.MP<RN D.MP>RN
Summary of this lesson
1. Our main study in this section is the rotational invariance of circles, that is, the relationship between central angles, chords, and arcs in congruent or equal circles.
2. We used methods such as folding, rotation, and proof.
Keywords: circle teaching courseware, circle symmetry teaching courseware, Beijing Normal University edition ninth grade mathematics volume 2 PPT courseware, ninth grade mathematics slide courseware download, circle PPT courseware download, circle symmetry PPT courseware download, .ppt format
For more information about the "Symmetry of Circles" PPT courseware, please click the Symmetry of Circles ppt circle ppt tag.
"Symmetry of Circles" PPT Courseware 2:
"Symmetry of a Circle" PPT courseware 2 Learning objectives: Understand the axial symmetry of a circle and its related properties; Understand the perpendicular diameter theorem; Be able to use the perpendicular diameter theorem to solve related problems. Key points and difficulties: The vertical diameter theorem and its applications. Communication and presentation of preview plans: knowledge preparation..
"Symmetry of Circles" PPT courseware:
"Symmetry of Circles" PPT courseware Class objectives 1. Experience the process of exploring the symmetry and related properties of circles. 2. Understand the symmetry and related properties of circles. 3. Understand the vertical diameter theorem and solve related problems. Review questions: 1. What is an axially symmetric figure? We are in a straight line...
"Symmetry of Circles" Circle PPT Courseware 3:
"Symmetry of Circles" Circle PPT Courseware 3 Learning Objectives 1. Fully grasp the axial symmetry of a circle through the combination of hands and brain. 2. Use exploration and reasoning to fully grasp the perpendicular diameter theorem and its inverse theorem in a circle. 3. Expand Thinking, combined with practice, using the vertical diameter theorem and its converse...
File Info
Update Time: 2024-07-06
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