To construct a square with sides of length AB, follow these steps:
- Draw Line Segment AB: Start by drawing a straight line segment that represents AB. Use a ruler for accuracy and label the endpoints as A and B.
- Construct Perpendicular Lines: At point A, use a compass and straightedge to construct a line that is perpendicular to the line segment AB. This can be done by placing the compass at point A, drawing an arc across line AB, and marking where it intersects. Without adjusting the compass width, place it at the intersection points and draw arcs above and below the line. The intersection of these arcs gives you a point that allows you to draw the perpendicular line.
- Measure Length AB: Use a compass to measure the length of segment AB. Keeping the compass width fixed, place the compass point on point A and draw an arc intersecting the perpendicular line. Label this intersection point as C. This ensures AC is equal to AB.
- Repeat for Point B: Now, repeat the process at point B to construct another perpendicular line. Again, measure the length of AB with the compass, and from point B, construct the intersection point on the perpendicular line. Label this new intersection point as D.
- Connect the Points: Finally, connect points C and D with a straight line to complete the square. You will now have points A, B, C, and D forming a square where each side is of equal length AB.
That’s it! You’ve successfully constructed a square with sides of length AB.