We start with a given line segment AB> This will become one side of the square.
5. Draw a line from B through H.
This line is perpendicular to AB, so the angle ABH is a right angle (90°);
This will become the second side of the square
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See also the animated version.
| After doing this | Your work should look like this |
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We start with a given line segment AB> This will become one side of the square. |
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| Note. Steps 1 through 5 construct a perpendicular to line AB at the point B. This is the same construction as Constructing the perpendicular at a point on a line | |
| 1. Extend the line AB to the right. | |
| 2. Set the compasses on B and any convenient width. Scribe an arc on each side of B, creating the two points F and G. | |
| 3. With the compasses on G and any convenient width, draw an arc above the point B. | |
| 4. Without changing the compasses' width, place the compasses on F and draw an arc above B, crossing the previous arc, and creating point H | |
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5. Draw a line from B through H. This line is perpendicular to AB, so the angle ABH is a right angle (90°); This will become the second side of the square |
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| We now create four sides of the square the same length as AB | |
| 6. Set the compasses on A and set its width to AB. This width will be held unchanged as we create the square's other three sides. | |
| 7. Draw an arc above point A. | |
| 8. Without changing the width, move the compasses to point B. Draw an arc across BH creating point C - a vertex of the square. | |
| 9. Without changing the width, move the compasses to C. Draw an arc to the left of C across the exiting arc, creating point D - a vertex of the square. | |
| 10. Draw the lines CD and AD | |
| Done. ABCD is a square where each side has a length AB | |