A graphic method for drawing a triangle with known three side lengths using geometric sketchpad

For example, it is known that the lengths of the three sides of a triangle are 3, 4, and 5. The specific operations are as follows:

1. Open the geometric sketchpad, execute [Data]-[New Parameter], and create a new parameter a=3; b=4;c=5, select [Distance] as the unit; select parameter a, execute [Transform] - [Mark Distance].

2. Use [Point Tool] to draw a point and select it, execute [Transform] - [Translation], set the angle to 0, and get another point.

3. Select the two points above and execute the [Construction] - [Line Segment] command to construct a line segment and obtain a line segment with a fixed length of 3.

4. Select one endpoint of the line segment with a length of 3 and parameter b, execute [Construction] - [Draw a circle with center and radius] to draw a circle, and then select the other endpoint of the line segment and parameter c, execute [Construction] - [Draw a circle with center and radius] to draw a circle. The intersection of the two circles is the third vertex of the triangle.

5. Use the [Line Segment Tool] to connect the endpoints and intersection points of the line segments to obtain a triangle with three sides of 3, 4, and 5. Finally, just hide unnecessary objects.

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