How to Make a Square With a Compass in a Rectangle
A square is a rectangle with all four sides having equal length. Use a compass to construct a square within a rectangle by drawing a series of arcs. The first arc locates a point along one side of the rectangle that is the same length as the adjacent side. Draw intersecting arcs in order to make a line perpendicular to this point. This line will divide the rectangle into a square and another rectangle.
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Instructions
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1
Place the needle of the compass at one corner of the rectangle (hereafter referred to as point P). Extend the compass hinge and place the pencil on the corner nearest to the corner on which you placed the needle (hereafter referred to as point Q).
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2
Draw an arc with the pencil from point Q through the inside of the rectangle to the opposite side. Label the intersection of the arc and the side of the rectangle point A.
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3
Place the needle of the compass on point A. Extend the hinge of the compass so that the pencil goes beyond the opposite side of the rectangle.
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4
Draw arcs intersecting the opposite side of the rectangle at two different points without adjusting the hinge. Label the points B and C.
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5
Place the needle of the compass on point B. Extend the hinge so that the pencil is slightly more than half the distance to point C. Draw a large arc from the side of the rectangle in either direction.
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6
Place the needle of the compass on point C without adjusting the hinge. Draw an arc that intersects the arc drawn in Step 5. Label the intersection of the two arcs point D.
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7
Draw a straight line connecting point A and D with your ruler. This line will subdivide the rectangle into a square and a rectangle. The square is formed by points P, Q and the segment of line AD within the rectangle.
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References
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