"Related Properties of Circles" Circle PPT Courseware 3

Description

"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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"Related Properties of Circles" Circle PPT Courseware 5:

"Related Properties of Circles" Circle PPT Courseware 5 Class Training 1. As shown in the figure, in ⊙O, the length of chord AB is 8cm, and the distance from the center O to AB is 3cm, then the radius of ⊙O is _____. 2. As shown in the figure, in ⊙O, CD is the diameter, EA=EB. Please come up with three correct conclusions_____..

"Related Properties of Circles" Circle PPT Courseware 4:

"Related Properties of Circles" Circle PPT Courseware 4 Question: What is the relationship between the degrees of the circumferential angles and the corresponding number of angles at the center of the circle? (1) When the center of the circle is on one side of the circumferential angle, prove: (The center of the circle is on the circumferential angle) Conclusion: The circumferential angle subtended by an arc is equal to one of the central angle it subtends..

"Related Properties of Circles" Circle PPT Courseware 2:

"Related Properties of Circles" Circle PPT Courseware 2 Can you find the center of a circular piece of paper without using any tools? What characteristics of a circle can you get from this? It can be found that the circle is an axially symmetrical figure. The straight line on which any diameter lies is its axis of symmetry. Explore and discover...

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Update Time: 2024-07-06

This template belongs to Mathematics courseware People's Education Press Ninth Grade Mathematics Volume 1 industry PPT template

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