Square Construction

Explore the geometric properties of a square

Summarize the properties of a square before you start your actual construction. Hint: If you are not familiar with the construction steps necessary for a square construction, you might want to explore the applet below. Just use the buttons of the Navigation Bar in order to replay the construction steps.

Task

Construct a square that passes the Drag Test by following the construction steps provided below.

Try it yourself...

Construction steps

1.	Draw the segment a = AB between points A and B.	7.	Intersect the perpendicular line d with circle e to get the intersection points E and F.
2.	Construct a perpendicular line b to segment AB through point B.	8.	Rename point E so it is called D.
3.	Construct a circle c with center B through point A.	9.	Create the polygon ABCD.
4.	Intersect the perpendicular line b with the circle c to get the intersection points C and D.	10.	Hide circles and perpendicular lines.
5.	Construct a perpendicular line d to segment AB through point A.	11.	Perform the Drag Test to check if your construction is correct.
6.	Construct a circle e with center A through point B.	12.	Enhance your construction using the Style Bar.