Question

1. Look at the figure. Which construction is illustrated?

Answer 1

The construction illustrated in the figure is that of a line parallel to $\overrightarrow{HJ}$ 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 $\overrightarrow{HJ}$.

The figure also contains arcs made by a compass that measures the angle between $\overrightarrow{HJ}$ and $\overrightarrow{HN}$. These arcs have been replicated at the point N on the straight line $\overrightarrow{HN}$.

This implies that the straight line through N has been constructed in such a way, so that the angle between that straight line and $\overrightarrow{HN}$ is equal to the angle between $\overrightarrow{HJ}$ and $\overrightarrow{HN}$. This makes these angles, corresponding angles and $\overrightarrow{HN}$ as the transversal. Thus, the new straight line is constructed parallel to $\overrightarrow{HJ}$.

A strong counterargument that this illustration is not that of a line perpendicular to $\overrightarrow{HJ}$ through point N is that the figure does not contain any straight line perpendicular to $\overrightarrow{HJ}$.

Thus, the construction illustrated in the figure is that of a line parallel to $\overrightarrow{HJ}$ through the point N.

Learn more about construction of parallel lines here:

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