Construct an equilateral triangle,given its side and justify the construction.

(N/A) Let us construct an equilateral triangle,each of whose side $= PQ$.
Steps of construction:
$I.$ Draw a ray $\overrightarrow{OA}$.
$II.$ Taking $O$ as centre and radius equal to $PQ$,draw an arc to cut $OA$ at $B$ such that $OB = PQ$.
$III.$ Taking $O$ as centre and radius $PQ$,draw an arc. Then,taking $B$ as centre and radius $PQ$,draw another arc to intersect the previous arc at $C$.
$IV.$ Join $OC$ and $BC$.
Thus,$\Delta OBC$ is the required equilateral triangle.
Justification:
By construction,$OB = PQ$ and $OC = PQ$ (radii of the same arc).
Also,$BC = PQ$ (radius of the arc with centre $B$).
Therefore,$OB = OC = BC = PQ$.
Since all three sides are equal,$\Delta OBC$ is an equilateral triangle.