A graphic method for drawing three equal line segments using geometric sketchpad

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Construct line segments. Use the Line Segment Tool to draw two known line segments and mark one of them AB.

Construct ray. With point A as the endpoint, use the ray tool in the line segment ruler tool to draw a ray AC.

Select the construction circle. Select point A and the unnamed line segment, select [Construction] - [Draw a circle with center and radius], then select [Draw a circle with center and radius], and the intersection point with ray AC is D. In the same way, draw a circle with point E as the center and line segment AC as the radius. In the same way, draw a circle with point E as the center and line segment AF as the radius.

Construct line segment FB. Select point D and line segment FB, select [Construction]-[Parallel Line] to construct the parallel line of FB. Use the same method to draw a parallel line from FB through point E. The intersection points of the two parallel lines and AB are G and H respectively. Points G and H are two trisection points.

Hide redundant objects. Select the extra line segments, circles and points, and press [Ctrl H] to hide them.

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