| Construction Algorithm | ||
| 1 |  |
Construct a line AC as a given diagonal of the square. |
| 2 |  |
Construct M as a midpoint of the diagonal AC. |
| 3 |  |
Construct the perpendicular line at M. |
| 4 |  |
Define a rotation with center M and angle 90° using menu item "Mode/Transformation /Rotation". |
| 5 |  |
Rotate the points A and C with the defined rotation to construct the points B and D. |
| 6 |  |
Join up the four points A, B, C and D to get the required square. |
| 7 | |
Switch to drag mode. Pick a free element. Move it around to check your construction. |
| Construction Theorems | ||
| The two diagonals of the square are perpendicular to each other and equal in length. Rotation preserves the distance between points. |
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