Construct a square using compass and straightedge. Follow the given steps below.
Step 1. Extend the line segment AB to the right.
Step 2. Point the compass on B and in any convenient opening draw an arc on each side of B creating the two points F and G.
Step 3. With the compass on G and any convenient opening, draw an arc above point B.
Step 4. Without changing the compass setting, place the compass on F and draw an arc above B, crossing the previous arc, and creating point H.
Step 5. Draw a line from B through H. This will become the second side of the square. This line is perpendicular to AB, SO ZABH is a right angle (90°).
Step 6. Set the compass on A and set its width to AB. This width will be held unchanged as we create the square’s other three sides.
Step 7. Draw an arc above point A.
Step 8. Without changing the setting, move the compass to point B. Draw an arc across BH creating point C-a vertex of the square.
Step 9. Without changing the setting, move the compass to C. Draw an arc to the left of C crossing another arc, creating point D- vertex of the square.
Step 10. Draw the lines CD and AD. These are the third and fourth sides of the square.