TO CONSTRUCT SQARES

A) By using Ruler and set square:

 1. Using a ruler or T-Square, draw a line segment AB corresponding to the length of one side of the square.

2. Place the set square at one end of the line segment (i.e., A) and draw a perpendicular line that is longer than the side of the square.

3. Using the ruler, mark a point on this line that corresponds to the length of the side of the square.

4. Place the set square at another end of the line segment (i.e., B) and draw a perpendicular line that is longer than the side of the square.

5. Using the ruler, mark a point on this line that corresponds to the length of the side of the square.

6. Using the ruler, connect the two marks made in steps 3 and 5 to form the square.

B) By using T-square and set square:

1. Using a ruler or T-Square, draw a line segment AB corresponding to the length of one side.

2. At A and B draw verticals AE and BF

3.  From point A draw a line  inclined at 45 to AB, Cutting line BF at C.

4.  From point B draw a line  inclined at 45 to AB, Cutting line AE at D.

5. Draw a line connecting C and D.

6. Then ABCD is the required square.

C) By using compass:

1. Draw a line segment AB corresponding to the length of one side.

2. At A, draw a line AE perpendicular to AB.

3. With centre A, and radius AB, draw an arc cutting AE a D.

4. With centre B, and radius AB, draw an arc.

5. With centre D, and same radius draw an arc cutting previously draw arc from B.

6. Mark the intersecting point as C.

7. Draw lines C with B, C with D.

8. Then ABCD is the required square.

TO DIVIDE A LINE

To divide a line segment into equal number of parts using a compass only, Example Divide the line into 5 parts,

Steps of construction:

1) Draw a line segment AB of any length.

2) Draw any ray AX, making an acute angle (angle less than 90°) with AB.

3) Now take a compass and with any length draw an arc cutting the line ray AX at point 1, mark this point as A1.

4) With the length A1, Draw 4 more arcs with centres 1, 2, 3, 4 as shown and mark those intersecting points as A2, A3, A4, A5 as shown below.

AA1 = A1A2 = A2A3 = A3A4 = A4A5

5) Now join BA5, it will form a triangle, similarly draw lines from the remaining 4 arcs parallel to line BA5 as shown.

6) The above points divide the line AB into equal parts (You can cross check by measuring the distances).