| Construction Algorithm | ||
| 1 |  |
Construct a line AB as a given base of the square. |
| 2 |  |
Construct a line at B so that it makes an angle 135° (measured anti-clockwise) with the base AB. |
| 3 | |
Construct another line at A so that it makes an angle 45°(measured anti-clockwise) with the base AB. |
| 4 |  |
Generate the intersection point between the two constructed lines in steps 2 and 3 at M. |
| 5 |  |
Define a rotation with center M and angle 90° using menu item "Mode/Transformation /Rotation". |
| 6 | |
Rotate the point B by the defined rotation to construct the vertex C, then rotate the point C to get the fourth vertex D of the square. |
| 7 |  |
Join up the four points A, B, C and D to get the required square. |
| 8 |  |
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. Each diagonal of the square bisects two opposite angles. Rotation preserves the distance between points. |
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