Draw a Square

A square is a quadrilateral with four right angles and four congruent sides. Easy to draw, right? Not so fast. Drawing a perfect square requires more than just a steady hand. Learning to draw a perfect square using either a protractor or compass is a useful skill.

Steps

Protractor Method

  1. Draw a side of the square using ruler. Keep track of the length of this side so you can make all four sides the same length.
  2. Considering the side drawn in the previous step as one of the arms, construct a right angle on each end of it. Thus the end points of the side drawn in the previous step would also be the two vertices of these right angles.
  3. Mark a point on each of the newly drawn arms (of the two right angles), at a distance (measured from the respective vertex of the right angle) which is same as the length of the side drawn initially.
    • Join these two points.
  4. You just drew a perfect square! Erase any extraneous constructions if you so wish.

Compass Method

  1. Construct a right angle (let's name it LMN) as described Construct-a-90-Degrees-Angle-Using-Compass-and-Ruler. Ensure that each of the arms are longer than the desired side length of the square.
  2. Place spike of the compass on the vertex of the right angle constructed in the previous step, i.e. on the point M, and set the width of the compass equal to the desired side length of the square - this set width remains unchanged until the entire construction is completed.
    • Draw an arc cutting the arm MN at some point (say P)
    • Draw another arc to cut the arm LM at some point (say Q)
  3. Place the spike of the compass on point Q and draw an arc somewhere below the arm MN.
  4. Place the spike of the compass on point P and draw another arc which cuts the arc drawn in the previous step at some point (say R).
  5. Connect the points P and R and the points Q and R using a straightedge.
    • The figure PMQR is a square. You may erase other unnecessary constructions if you so wish.

Things You'll Need

  • Paper
  • Ruler
  • Protractor or Compass
  • Pen or Pencil

Tips

  • Do not always erase the construction lines, sometimes your teacher wants work to be shown.

Warnings

  • The spike on a regular compass is potentially a safety hazard. Don't poke people with it, throw it across the room, or do anything else that could cause injury. If you are not experienced with using one, exercise increased caution.

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