This page shows how to construct a perpendicular to a line through an external point, using only a compass and straightedge or ruler. It works by creating a line segment on the given line, then bisecting it. The bisector will be a right angles to the given line. (See proof below).
The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.
The image below is the final drawing above with the red lines added.
|1||Segment RP is congruent to RQ||They were both drawn with the same compass width|
|2||Segment SQ is congruent SP||They were both drawn with the same compass width|
|3||Triangle RQS is congruent to triangle RPS||Three sides congruent (sss), RS is common to both.|
|4||Angle JRQ is congruent to JRP||CPCTC. Corresponding parts of congruent triangles are congruent.|
|5||Triangle RJQ is congruent to triangle RJP||Two sides and included angle congruent (SAS), RJ is common to both.|
|6||Angle RJP and RJQ are congruent||CPCTC. Corresponding parts of congruent triangles are congruent.|
|7||Angle RJP and RJQ are 90°||They are congruent and supplementary (add to 180°).|