Perpendicular at a point on a line
Geometry construction using a compass and straightedge
This page shows how to draw a
at a point on a line with compass and straightedge or ruler. It works by effectively creating two
and then drawing a line between their
Printable step-by-step instructions
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.
Segment KP is
congruent to KQ They were both drawn with the same compass width
Segment PR is
congruent to QR They were both drawn with the same compass width
Triangles ∆KRP and ∆KRQ are
Three sides congruent (sss). KR is common to both.
Angles PKR, QKR are
CPCTC. Corresponding parts of congruent triangles are congruent
Angles PKR QKR are both 90°
They are a
and (so add to 180°)
and congruent (so each must be 90°)
Try it yourself
Click here for a printable construction worksheet containing two 'perpendiculars from a point' problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Constructions pages on this site
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