| Construction Algorithm | ||
| 1 |  |
Construct a line AC as a given diagonal of the rectangle. |
| 2 |  |
Construct a line at C so that it makes an angle of 135° measured anti-clockwise with the diagonal AC. |
| 3 | |
Construct another line at A so that it makes an angle of 45° measured anti-clockwise with the diagonal AC. |
| 4 |  |
Generate the intersection point between the two constructed lines in steps 2 and 3 at B. |
| 5 |  |
Construct the image of B by reflection on AC to find the fourth vertex D of the square. |
| 6 |  |
Join up the four points A, B, C and D to get the required rectangle. |
| 7 |  |
Switch to Move 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. Reflection preserves the distance between points. |
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