Detailed steps for drawing a regular square prism on geometric sketchpad

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1. Create a new geometric sketchpad file. Draw line segments AB and BC. Select points B and C in turn, and select the [Transform]-[Mark Vector] command.

2. Select line segment AB, select the [Transform]-[Translation] command, and translate line segment AB according to the marker vector. Change the generated point A’ to D.

3. Draw the parallelogram ABCD and the diagonals AC and BD, and set the intersection of the line segments AC and BD to O. As shown below.

4. Draw a line segment DE arbitrarily. Select points D and E in turn and set them as [mark vector]. Translate point O in the direction of the marked vector to obtain point O’.

5. Draw line segments AO’, BO’, CO’, DO’, and OO’. Set the line segments OO’, DO’, AD, CD, AC, and BD as dotted lines.

6. Pick any point F on line segment DE, select points E, D, and F in sequence, and select the [Transform]-[Mark Ratio] command. Double-click point O’ and set point O’ as the center. Select points A, B, C, and D respectively, and select the [Transform]-[Scale] command to obtain points A’, B’, C’, and D’. Draw line segments A’B’, B’C’, C’D’, D’A’.

7. Hide redundant objects. Select the line segments AO’, BO’, CO’, DO’, OO’, DE and points O’, E, and select the [Show]-[Hide Object] command. Draw line segments AA’, BB’, CC’, DD’. Set DD’ to dashed line. In this way, the drawing of the regular square prism is completed. When we adjust the position of point F, we can observe that the square prism is also changing.

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