Question

Construct a square in which each diagonal is 5 cm long.

Answer 1

Steps of Construction
Step I Draw AC = 5 cm.
Step II With A as center, draw an arc of the length slightly greater than $\frac{1}{2}$ AC above and below the line segment AC.
Step III With C as center, draw an arc of the same length as in step II above and below the line segment AC which intersects the arcs drawn in step II.
Step IV Join both the intersection points obtained in step III by a line segment which intersects AC at O (say).
Step V With O as centre cut-off OB = OD = 2.5 cm along the bisector line.
Step VI Join AD, CD, AB and CB.
This is the required square ABCD.