In middle school mathematics, when learning geometric knowledge, it is often necessary to study a certain geometric figure in equal parts, such as bisecting line segments, bisecting triangles and so on. Now, to realize the trisection of a certain figure, there is no need to draw a ruler on the blackboard. It can be easily achieved by using the geometric sketchpad.
Geometric Sketchpad software access address : http://www.jihehuaban.com.cn/xiazai.html
Method 1 Use the zoom command
You can mark one endpoint of the line segment as the center, select the other endpoint, execute the "Transform" - "Scale" command, the scaling ratio is 1:3, and then scale it again, the ratio is 2:3.
Step 1 Open the Geometric Sketchpad courseware making tool , draw an equilateral triangle ABC, double-click point B to mark it as the zoom center, select point C, execute the "Transform" - "Scale" command, and enter the scaling ratio as 1 in the pop-up dialog box: 3. Click "OK" to get the third point D.
Example of executing the zoom command to get the trisection point D of the edge BC
Step 2 Then select point C, execute the "Transform" - "Scale" command, enter the scaling ratio as 2:3 in the pop-up dialog box, and click "OK" to get the third point E.
Example of executing the zoom command to get the trisection point E of the edge BC
Reminder: According to the above steps, you can find the trisection point of each side for research, so I won't introduce it here.
method two-point method
Use the value of the point to draw a point on the edge of the equilateral triangle, right-click on the edge, execute the "Draw Point on Line Segment" command, and enter "1/3" and "2/3" respectively.
Step 1 Draw an equilateral triangle ABC, use the "point tool" to draw a point D on the side BC, and execute the "measure" - "point value" command to get the value of the point on the side BC.
Example of value of point D on measure edge BC
Step 2 Select the edge BC, right-click the mouse, select the "Draw point on the line segment" command, enter "1/3" in the pop-up dialog box, click to draw, and get the third point E.
Example of Plotting Trisection Points Using Point Values
Step 3 Then execute the command again and enter "2/3", click Draw, and then click Finish to get the trisecting point F of side BC, as shown in the following figure. In addition, you can also use the geometric sketchpad to bisect the line segment, please refer to: How to use the geometric sketchpad to divide the line segment into three equal parts .
Example of drawing a trisection point F using the value of the point
Reminder: According to the above method, the trisection points of the remaining two sides can be constructed, which will not be described in detail here.
After reading the above tutorial, I have mastered two methods of constructing trisection points. The first method is relatively simple and can be completed by using the zoom command. You can master it with a lot of practice.
The above tutorials are referenced from: http://www.jihehuaban.com.cn/xinshourumen/sandeng-fen.html