To construct a square with sides of length AB, follow the steps below:
1. Place the compass at point A and draw an arc that intersects segment AB. Label the intersection point as C.
2. Without changing the compass width, move the compass to point C and draw another arc that intersects the previous arc. Label the intersection point as D.
3. Using a straightedge, draw a line segment from point C to point D. This line segment should pass through point B.
4. Construct perpendicular bisectors of segments AB and CD. To do this, place the compass at point A and draw arcs above and below segment AB. Repeat this step by placing the compass at point B and drawing arcs both above and below segment AB. With a straightedge, draw a line that connects the intersections of these arcs. This line will be the perpendicular bisector of segment AB. Repeat the same steps with segment CD to find its perpendicular bisector.
5. Let the perpendicular bisectors of segments AB and CD intersect at point E. Point E will be the center of the square.
6. Finally, draw lines from point E to the four corners of the square (points A, B, C, and D). These lines will form the sides of the square, with each side being of length AB.
The resulting figure will be a square with sides of length AB.
Given segment AB, explain how to construct a square with sides of length AB.
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