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Constructing a perpendicular at a point
This demonstration shows how to draw a
perpendicular to a line from a point on that line, using
only a compass and straight edge. See " Introduction to Euclidean Constructions"
We start with a line and point K on that line.
The result is a vertical line at 90° to the first, intersecting it at K.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
Step-by-step Instructions
| Step 1 |
Set the compass width to a medium setting. The actual width does not matter. |
| Step 2 |
Without changing the compass width, mark a short arc on the line at each side of the point K, forming the points P,Q.
These two points are thus the same distance from K. |
| Step 3 |
Increase the compass to almost double its width (again the exact setting is not important). |
| Step 4 |
From P, mark off a short arc above K |
| Step 5 |
Without changing the compass width repeat from the point Q so that the the two arcs cross each other, creating the point R |
| Step 6 |
Using the straight edge, draw a line from K to where the arcs cross. |
Explanation
This construction creates two congruent triangles QKR and PKR.
Since the angles ∠RKP and ∠RKQ are equal and form a
linear pair, they must both 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.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page
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