## Geometric Constructions using Your Compass And Ruler

Apart from just drawing circles, you can use your compass to do several other nifty things which can save you time.

### Bisecting an angle

Bisect means to cut something in two.  You can use your compass and ruler to split any angle up into two equal angles.  So if we start with:

First up, you need to put the sharp tip of the compass on the point where the angle starts (point A) and draw a small arc across like this:

Then put the sharp tip of the compass at point B and draw a small arc roughly in the middle of the angle.  Do the same for point C – don’t change the compass setting in between! The two arcs should cross over each other:

If you draw a straight line from point A through the intersection of these two arcs, you’ll have a line that exactly bisects the 60° angle:

### Bisecting a line

Sometimes you will want to split a line up into two equal length bits, like this one:

Set the compass so that the radius of any circle you draw is going to be a bit more than half the length of your line.  First put the compass point at A and draw an arc through the straight line.  Then put the compass at point B and repeat.  The two points where the arcs intersect can be joined by a straight line to split your original line into two equal parts:

### Drawing a perpendicular from a point on a line

Sometimes you need to draw a line starting from another line that is perpendicular.  You can use your ruler to do it, but it won’t be too good.  Or you can use your compass and ruler.  First you start with a line, and a point from which you want to draw the new perpendicular line (point B here):

Put your compass tip on point B, and draw most of a circle, making sure that it crosses over the straight line on both sides of point B:

Next thing to do is extend the compass radius by a bit, then place the compass tip at point A, and draw a small arc above point B.  Do the same thing after putting the compass tip at point C.  You should get the two arcs intersecting.  If you draw a line from point B to the intersection point, you’ve just constructed your perpendicular line:

### Drawing a perpendicular from a point to a line

Sometimes you’re given a point away from a straight line, and asked to draw a line from the point to the straight line which is perpendicular to the straight line.

First thing you need to do is set the compass radius so that it’s a bit longer than the shortest distance from point A to the line.  Then put the compass tip at point A and draw an arc which crosses through the straight line twice, like this:

Now put the compass tip at point B, and draw an arc above the straight line that is roughly in line vertically with point A.  Do the same thing for point C.  If you then draw a straight line from point A to the intersection point of the two arcs, you’ll have constructed your perpendicular.