Such as line segment AB

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JulianMathHelp

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So I got this problem where I was given a diagram, and it said what else can you construct when given a line segment such as AB. Does this mean What polygons/special lines can I construct given a line segment anywhere on the diagram, or at the exact segment where AB is? Basically what I'm asking is if the line segment HAS to have the endpoints as the center of the circles like AB does.

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What tools are you allowed to use? Ruler and compass? I would consider using the intersection points of the circles.
I don't think you have to be limited to the segment AB - it's already there!
 
So the segments could be anywhere? So one segment Could be like from one side of a circle all the way to the oppposite side of the other circle? Wouldn't the answer be different than if you were to use the intersection of the circles? Yes, it is a ruler and compass.
 
JulianMathHelp said:
So the segments could be anywhere? So one segment Could be like from one side of a circle all the way to the oppposite side of the other circle? Wouldn't the answer be different than if you were to use the intersection of the circles? Yes, it is a ruler and compass.
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I think the new segments can be anywhere. The end points should probably be A, B and any new points you construct by intersecting lines and arcs.
 
Didn't you say that the endpoints does't have to be A and B? And shouldn't it not be if the new segments can be anywhere. Also, if it can be anywhere, how would I solve this problem as there are multiple?
 
JulianMathHelp said:
Didn't you say that the endpoints does't have to be A and B? And shouldn't it not be if the new segments can be anywhere. Also, if it can be anywhere, how would I solve this problem as there are multiple?
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I said the new segments don't have to be AB since it's already there. Well, you can actually draw AB since it's being referenced but hasn't been drawn. So, you can still use A or B with _other_ points for new segments.
I think the problem is not to find some hidden segment, but to be creative and construct something.
 
I don't think the question "what else can you construct?" is looking for a specific answer. Different people can construct different things, they will all be correct, as long as they follow the rules (use the tools provided, etc).
 
Ok, so I could say that if we were given a segment, we can construct an Isosceles triangle and equilateral triangle even though in some circumstances it may not be as easy to construct?
 
Like if we were given AB it would be super easy to construct while if we were given a different segment, it would not be so easy.
 
JulianMathHelp said:
Like if we were given AB it would be super easy to construct while if we were given a different segment, it would not be so easy.
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Given any segment we can _always_ construct the two circles in the diagram. Not sure what you mean by "different segment". AB is an arbitrary segment, exactly like any other segment.
Regarding the previous question, what circumstances are you referring to? We are starting with a segment. We construct 2 circles. Then you add more lines, circles, points. You could not get any other circumstances if you tried.
 
Im talking about having a segment like:Screen Shot 2020-04-21 at 3.34.44 PM.png If we were given the segment AB to work with to construct something new, you can easily make an isosceles triangle, on the other hand, if we were given a segment like GF, how would we construct the isosceles triangle.

The literal wording of the problem is: What else can this diagram help you construct when given a line segment such as AB¯? Share your ideas with the class.
 
JulianMathHelp said:
Im talking about having a segment like:View attachment 18088 If we were given the segment AB to work with to construct something new, you can easily make an isosceles triangle, on the other hand, if we were given a segment like GF, how would we construct the isosceles triangle.

The literal wording of the problem is: What else can this diagram help you construct when given a line segment such as AB¯? Share your ideas with the class.
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You are given only segment AB. The circles are constructed based on it, do you see how? The segment came first, not the circles.
 
So the segment that they are giving in THIS problem is AB? Also in the problem it constructed the circles first where points A and B are centers of each circle.
 
JulianMathHelp said:
The literal wording of the problem is: What else can this diagram help you construct when given a line segment such as AB¯? Share your ideas with the class.
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So why didn't you state the complete problem from the start? Do you not see how important that is?? You said nothing about the diagram playing a specific role. Not stating the problem wastes people's time.

If you are given a segment AB, and then construct the two circles, what might you do next? Can you join some points and make something else of interest, such as a particular kind of triangle or quadrilateral, or some related line? There are indeed several answers.
 
Ok so what is really bothering me is the wording: "When given a line segment such as AB". This bothers me because what does it mean by SUCH AS AB? Because, if you are given any line segment on this diagram, most of the time you wouldn't be able to utilize the diagram.
 
JulianMathHelp said:
Ok so what is really bothering me is the wording: "When given a line segment such as AB". This bothers me because what does it mean by SUCH AS AB? Because, if you are given any line segment on this diagram, most of the time you wouldn't be able to utilize the diagram.
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You are given a segment. Period. Nothing else. Then someone constructed the 2 circles. Now you are asked to continue constructing stuff. Go ahead.
 
Does it make a difference if two circles were constructed first? Then they named the points and made the segment?
 
JulianMathHelp said:
Does it make a difference if two circles were constructed first? Then they named the points and made the segment?
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Yes, it does. And it would be an interesting exercise to ponder. For example, we would not know that the circles have equal radius.

I don't see an ambiguity. You are asked "what else can you construct when given a line segment such as AB?"
Given a segment - we start with a segment.
What else - what do you think this else refers to if not the circles constructed based on the segment???
 
Okay, so I did some thinking, when they say "what else can you construct when given a line segment such as AB" it is asking what other constructions can we create when we are given a segment such as AB, and by saying such as AB, it is implying that we should use AB as the given segment in the scenario correct? If they didn't say "such as AB", then the problem would be pretty hard to answer as you wouldn't really know which segment to start off on, and there would literally be an infinite amount of answers. Also, in the problem, it is given that the circles were constructed first, with equal radius, and the points are assumed as the center. This is my understanding. Also, sorry for leaving out some important details, it won't happen again, and im sincerely sorry for wasting your time :(.
 
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