Construct a Square:

For Constructing a Square when Length of One Side is given

Along with a T-square and a set-square only in diagram (a) and AB being the length of one side of a square draw a line AB. Throughout A and B, draw vertical lines AM and BN. Draw from points A and B respectively, lines AC and BD inclined at 45o to AB, cutting BN at C and AM at D. Join C along with D. ABCD is the essential square.

Along via the aid of a compass in diagram (b) draw a given line AB. At A, draw a line AM perpendicular to AB. Along with A as the centre and radius AB, draw an arc cutting AM at D. along with B and D like the centers and containing the same radius, that is AB, draw arcs intersecting all other at C. Join BC and CD. ABCD is the essential square.

For Constructing a Square when the Length of a Diagonal is given

Draw the given diagonal AC or BD and bisect it. The bisecting line bisects the diagonal at O. Along with O as the center and the radius equal to OA or OC; draw a circle to cut the bisecting line at B and D. Join AB, BC, CD and DA to get ABCD as the essential square.