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Construct a Square, Given a Side


Use the tools in the applet to construct a square with AB as one of its sides. Explore. Try to do this on your own. If you need more help, there are detailed instructions and a video at the bottom.

How to Construct a Square

You start with segment AB. Use the LINE tool to make this line AB. Use the compass tool to make a circle from A to B (Center is at A). Mark the other intersection as point C. Segments AB and AC are congruent because both are radii of circle A. Construct two more circles. One is from C to B. The other is from B to C. Mark the points where these two circles intersect as D (on top) and E (on bottom). DE is the perpendicular bisector of segment BC. They intersect at right angles. This is important, because this will make part of our square. Mark the intersection of circle A and segment DA. Call it F. AF and AB are two sides of the square. Finally, make two more circles and their intersection: from D to A and from B to A. Call the intersection G. You should have ABGF is a square. Use the POLYGON tool to make it a square. Do the DRAG TEST to verify it is a square.

Construct a Square, Given a Side