Question

Rosa is trying to copy an angle. She reads and understands all of the steps, but insists on drawing circles instead of arcs. Which of the following is the best response to tell Rosa?

A. It is acceptable to draw circles instead of arcs, but because they are bigger and take up more space, your drawing may become messy, increasing the chance for errors. <-- MY ANSWER

B. You have to use arcs because a compass cannot make a full circle.

C. You have to draw arcs because arcs and circles are not interchangeable.

D. She is right because it is better to draw circles than arcs. Circles are clearer and easier to draw than arcs so you are less likely to make a mistake.

Thanks!

Answer 1

You have the correct answer. It is choice A. Nice work.

I prefer using full circles because sometimes the arcs could be too small in measure to not go where you want them to. If you're worried about things getting too cluttered (a legitimate concern), then I recommend drawing everything in pencil and only doing the circles as faint lines you can erase later. Once the construction is complete, you would go over the stuff you want to keep with a darker pencil, pen or marker. You can also use the circle as a way to trace over an arc if needed.

Choice B is false as a full circle can be constructed with a compass. Simply rotate the compass a full 360 degrees. Any arc is a fractional portion of a circle.

Choice C is false for similar reasoning as choice B, and what I mentioned in the paragraph above.

Choice D contradicts choice A, so we can rule it out. Arcs are easier to draw since it takes less time/energy to rotate only a portion of 360 degrees. Also, as mentioned earlier, having many full circles tend to clutter things up.