What are the steps for using a compass and straightedge to construct a square?
1.) Determine the length that one side of the square should be.
2.) Using a writing utensil and straightedge draw said length in the form of a line segment.
3.) Depending on what the compass looks like there are two options.
(Scissor looking compass:) Draw a circle by placing the point at the middle of the line and rotating about the axis. Then draw an equivalent line segment length running from one side of the circle to the next. You should end up with a circle with a plus sign in it. From there simply move the lines out to the side and its done. Then finish up the square.
(Easier way:) Always remember that the vertices of a square are each 90 degrees.
So the other way, would be marking where a 90 degree angle is made from the line, and basically connecting the dots when done.
If you want an image check "square wikipedia"
The above instructions are rather murky at best. The key is to construct a right angle. There are lots of explanations on how to do this, such as the one at
http://www.mathopenref.com/constsquare.html
To construct a square using a compass and straightedge, follow these steps:
1. Start by drawing a line segment with the desired length of one side of the square using a straightedge.
2. Place the sharp end of the compass at one end of the line segment and open the compass to a width equal to the length of the line segment.
3. Without changing the compass width, draw an arc from the other end of the line segment to create an intersection point on the original line.
4. Now, place the sharp end of the compass on the newly created intersection point and draw arcs on both sides of the line segment. These arcs should intersect with each other and form two additional points.
5. Connect these two new intersection points with straight lines. You now have a rectangle.
6. Using the compass again, set the width to the distance between the endpoints of one of the shorter sides of the rectangle.
7. Place the sharp end of the compass on one endpoint and draw an arc that intersects one of the longer sides of the rectangle.
8. Without changing the compass width, place the sharp end of the compass on the other endpoint and draw another arc that intersects the longer side. These arcs should intersect with each other.
9. Connect the two new intersection points with a straight line segment. You now have a square.
By following these steps, you can construct a square using just a compass and straightedge.