Start with drawing a line and constructing a perpendicular line.
See solution.
Practice makes perfect
Let's start our construction of a rectangle with drawing a line l and label a point A. This point will be the first vertex of this rectangle.
Now we will construct a line perpendicular to l and passing through point A. Let's place the compass at A and draw arcs to the right and left of A using the same compass setting.
Next, with the compass at each of the points of intersection with line l, we will draw arcs above line l using a setting greater than a half of this segment.
Label the point of intersection of these arcs B, and connect the points A and B with a line m.
Now, we will construct a line perpendicular to m and passing through point B in the same way as before. Label this line n. Notice that lines l and n will be parallel as they are perpendicular to the same line.
Next, we will label another point on the line n that will be the third vertex C. With this we will place the compass in point B, and adjust the compass setting so that the pencil is at point C.
Using that setting let's place the compass point at A and draw an arc that intersects line l. Label this point of intersection D. This will be the fourth vertex of the rectangle.
Finally, we will connect points C and D with a segment. We ended our construction with a rectangle ABCD.
