Construction of Square

Construction of Square Given the Length of Sides:

Steps:

• Draw a line segment AB of a given length.

• Extend line AB to the right.

• Set the compasses on B and any convenient width. Draw an arc on each side of B, creating the two points E and F.

• With the compasses on F and any convenient width, draw an arc above point B.

• Without changing the compasses’ width, place the compasses on E and draw an arc above B, crossing the previous arc, and creating point G

• Draw a Line from B through G

• Set the compass to A and set its width to AB. This width will be held unchanged as we create the square’s other three sides.

• Draw an arc above point A (from point A) with the width AB as mentioned above.

• Without changing the width, move the compasses to point B. Draw an arc across BG creating point C – a vertex of the square.

• Without changing the width, move the compasses to C. Draw an arc to the left of C across the exiting arc, creating point D – a vertex of the square.

• Join CD and DA to complete the required square.

• ABCD is a square where each side has a length AB.

Construction of Square Given the Length of Its Diagonal:

Steps to Construct a square when a diagonal is given;

• Construct a line AC as a given diagonal of the square with a given length. e.g 10cm

• Bisect the line AC.

• Construct a circle centred at M and has a radius MC.

1. First measure the distance MC, which is half of AC e.g 5cm

2. Construct a circle centred at M with the radius from step 1 above. (Use a compass)

• Name the intersection points between the circle and the perpendicular line at M as B and D.

• Join up the four points A, B, C and D to get the required square.