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"Related Properties of Circles" Circle PPT Courseware 3
1. Thinking
Is a circle a centrally symmetrical figure? Where is its center of symmetry?
A circle is a centrally symmetrical figure, and its center of symmetry is the center of the circle.
Circles are rotationally invariant
2. Concept
Central angle: We call the angle whose vertex is at the center of the circle called the central angle.
∠AOB is the central angle of the circle
3. Exploration
According to the nature of rotation, when the central angle ∠AOB is rotated around the center O to the position of ∠A′OB′, it is obvious that ∠AOB = ∠A′OB′, rays OA and OA′ coincide, and OB and OB′ coincide. The radii of the same circles are equal, OA=OA', OB=OB', so points A and A' coincide, and B and B' coincide.
4. Theorem
In congruent circles or equal circles, the arcs subtended by equal central angles are equal, and the chords subtended by equal central angles are also equal.
In congruent or equal circles, if two arcs are equal, then the central angle they subtend is _____, and the chord they subtend is ________;
In congruent or equal circles, if two chords are equal, then the central angle they subtend is ______ and the arc they subtend is ________.
In congruent circles or equal circles, one set of quantities in two central angles, two arcs, and two chords are equal, and the other sets of quantities corresponding to them are also equal.
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