The construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through point N.
Given: Figure containing illustration of the construction
To find: The construction illustrated in the figure
It can be seen that the figure contains a straight line passing through H and J, a straight line passing through H and N, and a straight line passing through N which seems to be parallel to [tex]\overrightarrow{HJ}[/tex].
The figure also contains arcs made by a compass that measures the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. These arcs have been replicated at the point N on the straight line [tex]\overrightarrow{HN}[/tex].
This implies that the straight line through N has been constructed in such a way, so that the angle between that straight line and [tex]\overrightarrow{HN}[/tex] is equal to the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. This makes these angles, corresponding angles and [tex]\overrightarrow{HN}[/tex] as the transversal. Thus, the new straight line is constructed parallel to [tex]\overrightarrow{HJ}[/tex].
A strong counterargument that this illustration is not that of a line perpendicular to [tex]\overrightarrow{HJ}[/tex] through point N is that the figure does not contain any straight line perpendicular to [tex]\overrightarrow{HJ}[/tex].
Thus, the construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through the point N.
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