Copying angles with a drawing compass

file: AngleByCompass.htm

This essay shows you how to make a copy of an angle with just a compass and a ruler... and you only use the ruler to draw two straight lines.

Take the following slowly. There's a lot of words, but they really aren't asking for anything very complicated. If you are struggling, even just a bit, try doing the exercise with someone. One of you take charge of reading the instructions, step by step, and the other person will actually do the things the instructions call for, watched over by the instruction reader. You might be surprised by how much two heads are better than one on a job like this.

The following shows where we are headed. We are given the angle shown at the top, and our task is to make a copy of it, same size, below, where I've drawn it roughly with dotted lines.

We don't really care how long the arms are, but we want the "pointiness" of the copy to be as close as we can make it to the original.

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Start by drawing a line to be the B-C side of our new copy of the original angle. (I'm just using the compass's pencil for this. I'm not using "the compass part")

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Make a mark at one end of it. This will be where B is...

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Use a compass (set to any convenient distance) to make a small arc on the original angle. The point of the compass should be on B...

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Since the stage shown above, a second arc was done on the original angle on the A arm, the same distance from B as the first arc we drew.

The drawing below also shows arcs on the copy. They are copies of the arcs we put on the angle we are copying. There's a short arc (being drawn) on the line from B towards C, and a longer one (already drawn) on the part of the paper through which the line from B to A will go.

All of these arcs are done with the compass on the same setting.

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Now we change the distance between the compass's spike and its pencil. We set the compass to the distance from where the arc on the lower arm of the angle we are copying crosses that arm to where the other arc crosses its arm...

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Then we use the compass, set like that, to make a further arc, this one across the arc we made earlier, across the part of the page where the BA line will go...

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Nearly there! The line running from B towards A goes from B... you know that from the name!... through where the crossing arcs cross. I've circled these two important places in red. Line a ruler up on them, draw a line. That will produce an accurate copy of the angle we started with.

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Finished copy of the original angle...

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Notice something: We don't know "how big" the angle is! We haven't measured it. But we don't need to, to do an accurate copy.

The easy way to measure an angle is to use a protractor. But unless you spend lots of money on a well made, large protractor, you won't get a very precise reading.

You can make a quite accurate copy of an angle using the method given with even an ordinary compass. If you have one that can be "locked" at a particular setting, so much the better, but it really isn't necessary if you work carefully.

The larger you can make the distance from the apex of the angle ("B") to the four arcs you draw to start this, the more accurate your copy will be. (You should be able to see why. Think about it?)

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