Detailed steps for making a demonstration animation of the circumferential angle theorem on the geometric sketchpad

php editor Strawberry reveals to you the new game experience of Winter Rhapsody! This character plot simulation game set in a small town story incorporates Japanese elements, and players will face various in-depth puzzle-solving challenges. Skill operation becomes key, and unlocking all skills will give you a more comprehensive gaming experience. Are you ready to experience exciting special content and rich skill-based gameplay?

The circumferential angle theorem: The circumferential angle subtended by an arc is equal to half the angle subtended by it at the center of the circle.

The specific operation is as follows:

Use the "Circle Tool" to draw a circle O, and then use the "Point Tool" to pick any three points A, B, and P on the circle, and select points B, A and circle O, execute the "Construction" - "Arc on Circle" command to construct arc AB. Use the line segment tool to construct line segments OA, OB, PA, and PB, and make the circumferential angle and central angle. Note that the arcs they correspond to are the same.

Measures the central angle and circumferential angle in degrees. Select three points A, O, and B in order, execute the [Measure]-[Angle] command, and the size of ∠AOB will be displayed immediately in the upper left corner of the drawing board. The size of ∠APB can be measured in the same way. Once you do this, you can perform a manual demonstration.

At this time, manually demonstrate the courseware and use the mouse to move the position of point P. The degrees of the two angles will not change, and ∠AOB is twice that of ∠APB. Therefore, when ∠AOB is fixed, the theorem is established. Then students may ask: If the size of ∠AOB is changed, will there still be this quantitative relationship between these two angles?

Calculate the value. Execute the [Data]-[Calculate] command to calculate the value of ∠AOB/∠APB. At this time, move the position of point B and change the size of ∠AOB. The value of ∠AOB/∠APB is always equal to 2. This means that when the size of ∠AOB changes, ∠APB is still half of ∠AOB.

Set point animation. Manual demonstrations have location limitations and are difficult to convince students. Therefore, to set a point animation, first set the animation of moving point A, select point A, and execute the [Edit]-[Operation Button]-[Animation] command. Set the specific properties as shown in the figure below, click the animation button, It can be seen that no matter how the degrees of the two angles change, their ratio is always 2 and does not change.

Set the animation of another point P, indicating that no matter how point P moves on the circle, the ratio is 2. The setting method is the same as above. Just emphasize that if you want to change the label, click the label and name it animation point P.

Example of making animation by clicking the P button. Use and save animation. The courseware is ready. Click the animation point P button to explain that no matter how point P changes position, the degree of the circumferential angle is always equal to the degree of the central angle of the circle subtended by the same arc. Click the animation point A button, no matter how ∠AOB changes, the circumferential angle ∠APB will always be equal to one and a half of it. Finally, execute the [File]-[Save As] command to save the file, which can be inserted into PPT or used alone.

The above is the detailed content of Detailed steps for making a demonstration animation of the circumferential angle theorem on the geometric sketchpad. For more information, please follow other related articles on the PHP Chinese website!