Measuring an arc with a compass?

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JulianMathHelp

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Multiple Choice: Jamila has started to construct a line parallel to line m through point Q at right. Which of the possible strategies below make the most sense to help her find the line parallel to m through point Q?

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  1. Measure ∠QPR with a protractor.
  2. Use the compass to measure the arc centered at P, then place the point of the compass where the arc centered at Q meets QP¯, and mark that measure off on the arc.
  3. Construct QR¯.
  4. Measure PR with a ruler.

What does it mean to measure the arc centered at P? How do you measure the arc? Can someone explain B to me?
 

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It may be intended to be meaningless, so that that is not a valid choice.

Or they might mean measuring a chord of the arc; there is a way of constructing a duplicate angle by such means, though much more has to be said. But none of these has been fully described.

The whole thing requires further context. You appear to have been taught a notation that is unfamiliar to me. Can you tell me what is meant by [MATH]QP^-[/MATH] and [MATH]QR^-[/MATH]? Also, what "makes the most sense" is at some point a subjective judgment. I can't tell from what you show whether, for example, they want a theoretically exact parallel, or just a reasonable drawing.

Where does this come from?
 
JulianMathHelp said:
Multiple Choice: Jamila has started to construct a line parallel to line m through point Q at right. Which of the possible strategies below make the most sense to help her find the line parallel to m through point Q?

ccg_original.png

  1. Measure ∠QPR with a protractor.
  2. Use the compass to measure the arc centered at P, then place the point of the compass where the arc centered at Q meets QP¯, and mark that measure off on the arc.
  3. Construct QR¯.
  4. Measure PR with a ruler.

What does it mean to measure the arc centered at P? How do you measure the arc? Can someone explain B to me?
Click to expand...
Don't understand #2. Don't see how the rest help.
I would construct a point S, such that QPRS is a parallelogram. QS is the line you need.
 
Dr.Peterson said:
Or they might mean measuring a chord of the arc; there is a way of constructing a duplicate angle by such means, though much more has to be said. But none of these has been fully described.
Click to expand...

Wouldn't this strategy only work if both arcs have the same radius, as that would make both arcs congruent, meaning they have the same angle. However if one arc has a larger radius than the other, that wouldn't work, and with this problem, it doesn't tell us.

Dr.Peterson said:
You appear to have been taught a notation that is unfamiliar to me. Can you tell me what is meant by [MATH]QP^-[/MATH] and [MATH]QR^-[/MATH]?
Click to expand...

It just means segment, I copy pasted it onto here, and it turned out like that.
 
JulianMathHelp said:
How about the first option, wouldn't that one help by finding the angle, and with that, we would be able to copy it?
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Yes, if you are allowed to construct a line through a point, at a given angle to another line.
 
Surely you have learned how to use a straightedge and compass to duplicate a given angle at a given point???
 
JulianMathHelp said:
Wouldn't this strategy only work if both arcs have the same radius, as that would make both arcs congruent, meaning they have the same angle. However if one arc has a larger radius than the other, that wouldn't work, and with this problem, it doesn't tell us.
Click to expand...
That is exactly why I said that "much more has to be said." And that is part of why I think it's a poorly worded question.

(1) would allow you to then draw that angle at Q and approximately make the parallel line; it just wouldn't be theoretically precise, as they would want if this is from a section about exact constructions.
(2) is part of the standard duplication of an angle with compass and straightedge, if they had told us that the two arcs drawn have the same radius, and if "measure the arc" means what I suggested. Since you say you have learned that construction, and since it appears that that is what has been started, this may be what they want.
(3) seems useless by itself, but there is a valid construction of which that would be a part.
(4) also seems useless, it too could be used for an approximation construction with some other steps.

So what "makes the most sense"? That's up to you. It's a subjective question.

I myself would say that none of them are full "strategies", and all of them might conceivably be part of something bigger that would work.
 
"Would" means that I am leaving the final decision to you. "Would" is a modal verb that is typically used after "if".

I have told you I don't like the question itself. But if I had to make a choice, and not just complain to the publisher, and if the choices were a, b, c, d (rather than 1, 2, 3, 4 as shown), then I would answer (b).

Sorry for being too subtle.
 
t means that I am deliberately being evasive. It is your job to answer the question; I am here to help. I have told you my answer; but you need to make your own decision. Don't demand that other people do everything for you.

It also means that I am tired of the problem, which as I have said is poorly written, and I do not want to take responsibility for telling you what answer they want, when they can't write a problem clearly in the first place.

Literally, when I said "I would agree", I meant "I am generally inclined to say the same thing, but I am not willing to commit myself". Is that clearer?
 
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