| Construct square ABCD:

which has diagonal 6 cm.

which has a diagonal 6 cm.

Construction:

1) Find the side - length of the square using the length of the diagonal.

2) We know that for a square of side - length ‘a’, the length of diagonal is ‘a√2’.

3) From this, we can the length of the side is i.e, ‘3√2’cm.

4) So, now we draw a line segment ‘AB’ of length ‘3√2’cm.

5) Draw a line perpendicular to line segment ‘AB’ using protractor at point ‘B’.

6) Now, taking point ‘A’ as centre draw an arc of radius ‘6’cm.

7) The arc intersects the line at a point, this point is ‘C’.

8) Join points ‘A’, ’C’ to form the line segment ‘AC’ and points ‘B’, ’C’ to form line segment ‘BC’.

9) Now draw a perpendicular to the line segment ‘BC’ using protractor at point ‘C’.

10) Now draw a perpendicular to the line segment ‘AB’ using protractor at point ‘A’.

11) These two perpendiculars intersect at a point, this point is ‘D’.

12) Join points ‘C’, ’D’ to form line segment ‘CD’ and points ‘A’, ’D’ to form the line segment ‘AD’.

13) Thus square ‘ABCD’ is formed.

Allister:

1) Draw a horizontal line of the length of diagonal.

2) Mark a point as ‘A’ and from this point draw a line of length ‘6’ cm at an inclination of ‘45⁰’ with the horizontal line.

3) Now from the end of diagonal (i.e, Point ‘C’) draw a line of inclination of ‘45⁰’ with the diagonal in the direction of the horizontal line.

4) Now, the horizontal line and the line drawn towards the horizontal line will intersect at a point, this point is ‘B’.

5) Now draw a perpendicular to the line segment ‘BC’ using protractor at point ‘C’.

6) Now draw a perpendicular to the line segment ‘AB’ using protractor at point ‘A’.

7) Join points ‘A’, ’D’ to form the line segment ‘AD’ and points ‘C’, ’D’ to form line segment ‘CD’.

8) Thus square ‘ABCD’ is formed.