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Constructing perpendicularsConstructing perpendiculars to a line through a given point using only a straightedge and a compass is what I will show you here There are two cases that you may encounter Case #1: You are given a line and a point on the line   Let us start with case #1: Step #1 Start with the following line and point P   Open your compass to a radius or distance greater than the distance you chose to draw the arcs After you have increased your compass opening, place the needle at C and draw and arc Then, still using the same compass opening place the needle at D and draw another arc. The two arcs should intersect as shown below. Call the point the two arcs intersect E  Draw an line between P and E and you are done!  Start with the following line and point P not on the line  Open your compass to a radius or distance greater than the distance from P to the line. The distance you see below in red is the shortest distance from P to the line. That is what I mean by distance from P to the line; It is the shortest distance from P to the line which is usually done by drawing a straight line down  Step #2 After opening your compass to a distance greater than the shortest distance from P to the line, place the needle of the compass at P draw arcs that interset the line in two places  Step #3 Keeping the opening of the compass the same, place the needle at A and draw and arc Then, place the needle at B and draw an arc. Call the point the two arc intersect E.  Draw a line between point P and point E and you are done! 
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| Homepage|Straightedge and compass|
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|Copying an angle
|Bisecting an angle
|Constructing perpendiculars|
Constructing an equilateral triangle|
Constructing the midpoint of a segment |
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