How to construct (draw) a perpendicular at a point on a line

Perpendicular at a point on a line

Geometry construction using a compass and straightedge

- Printable problem worksheet
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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

	After doing this	Your work should look like this
	Start with a line and point K on that line.
1	Set the compass width to a medium setting. The actual width does not matter.
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.
3	Increase the compass to almost double its width (again the exact setting is not important).
4	From P, mark off a short arc above K
5	Without changing the compass width repeat from the point Q so that the the two arcs cross each other, creating the point R
6	Using the straight edge, draw a line from K to where the arcs cross.
7	Done. The line just drawn is a perpendicular to the line at K

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.

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