Describe at least two similarities between constructing a perpendicular line through a point on a line and constructing a perpendicular through a point off a line.

A perpendicular line is a required line that should be drawn at an angle of [tex]90^{o}[/tex] a given line. Thus some of the similarities that can be observed are:
i. The perpendicular line is at a right angle to the given line in each case considered.
ii. The perpendicular line may not be a bisector of the given line in each case.
iii. The perpendicular line intersects the given line at a point in each case.
A line is said to be perpendicular if it forms a right angle to a given line. Such that it intersects the given line at a point, and an angle [tex]90^{o}[/tex] is made at that point.
In the given question, the perpendicular lines referred to are not said to be bisectors, thus just at a right angle to a given line. A bisector is a line that cuts a given line into two equal parts.
Therefore, some required similarities between the two lines are:
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