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Authoritative PPT Summary
"Rotation of Plane Figures" PPT courseware
Get to know spin
rotation of graphics
Point A goes around point __, in the direction of ___, and rotates __ degrees to point B.
Rotating a figure by an angle in a certain direction around a fixed point in a plane is called rotation.
This fixed point is called the center of rotation, and the angle of rotation is called the angle of rotation.
If point A on the graph becomes B through rotation, then these two points are called the corresponding points of this rotation.
Three elements of rotation:
Rotation center, rotation angle, rotation direction.
Question: How to determine the angle of rotation?
Inquiry activities
Questions to explore:
1. Connect the corresponding points A, A/ and the rotation center O respectively, and measure the line segment OA and the line segment OA/. What is their relationship? Find any pair of corresponding points and measure the distance from the corresponding point to the rotation center. You can find What rules?
2. Measure the degree of ∠AOA/, then find any pair of corresponding points, and measure the angle between the corresponding points and the line segment connected to the center of rotation. What rules can you find?
Properties of rotation:
The distance between the corresponding point and the center of rotation is equal;
The angles formed by the lines connecting each pair of corresponding points and the center of rotation are equal angles, and they are equal to the angle of rotation.
Basic properties of rotation
◆The distance between the corresponding point and the center of rotation is equal.
◆The angles formed by the lines connecting each pair of corresponding points and the center of rotation are equal angles. They are all equal to the angle of rotation.
◆The rotation of the graphic is determined by the rotation center, rotation angle and rotation direction.
Discuss
As shown in the figure, if the pointer of the clock is regarded as a quadrilateral AOBC, it rotates around point O to obtain a quadrilateral DOEF. During this rotation process:
(1) What is the center of rotation?
(2) After rotation, where do points A and B move to?
(3) What is the rotation angle?
(4) What is the relationship between the length of AO and DO? What about BO and EO?
(5) What is the relationship between ∠AOD and ∠BOE?
Simple rotation drawing
Example 1 Rotate point A 60˚ clockwise around point O.
1. Connect OA, use a protractor or triangular plate (special angles only) to make ∠AOC, and intersect the circle at point B.
2. With point O as the center of the circle, the length of OA as the radius, draw an arc to intersect OB at point C;
3. Point C is the required operation.
Example 2 Rotate line segment AB 60˚ clockwise around point O.
practice:
1. Rotate point A 60˚ clockwise around point O to get point C;
2. Rotate point B 60˚ clockwise around point O to obtain point D;
3. Connect CD, then the line segment CD is the desired construction.
Class summary
1. Definition of rotation: In a plane, a graphics transformation that rotates a figure around a fixed point by an angle is called rotation. This fixed point is called the center of rotation, and the angle of rotation is called the angle of rotation.
2. Nature of rotation:
① Rotation does not change the size and shape of the graphic, but it can change the direction;
②The angle formed by the line connecting any pair of corresponding points of the two figures before and after the rotation and the center of rotation is the rotation angle.
③The distance between the corresponding point and the center of rotation is equal.
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"Rotation of Plane Figures" PPT Courseware 3:
"Rotation of Plane Figures" PPT Courseware 3 Think about it. What common characteristics do the rotation phenomena in the above scenario have? During the rotation of the hands and swings of the clock, their shapes and sizes...
"Rotation of Plane Figures" PPT courseware 2:
"Rotation of Plane Figures" PPT Courseware 2 Observation and Thinking 1. Observe how the hands of the clock in Figure 1 move from OA to OB position? 2. Observe the rotation process of the hands of the clock in Figure 2. Please tell how the blades of the windmill move from OM turns to the ON position? 3. As shown in the figure, the triangle AOB is...