This page shows how to draw a perpendicular at a point on a line with compass and straightedge or ruler. It works by effectively creating two congruent triangles and then drawing a line between their vertices.
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.
This construction works by effectively building two congruent triangles. The image below is the final drawing above with the red lines added.
|1||Segment KP is congruent to KQ||They were both drawn with the same compass width|
|2||Segment PR is congruent to QR||They were both drawn with the same compass width|
|3||Triangles ∆KRP and ∆KRQ are congruent||Three sides congruent (sss). KR is common to both.|
|4||Angles PKR, QKR are congruent||CPCTC. Corresponding parts of congruent triangles are congruent|
|5||Angles PKR QKR are both 90°||They are a linear pair and (so add to 180°) and congruent (so each must be 90°)|