Mathematical proof (Drawing a help line)

  • Thread starter Dousin12
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  • #1
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Homework Statement


I'm doing quite a strict proof in school. Where we should proof something and use mathematical language and symbols.

Homework Equations


97986e078015874b5c69ab8414038346.png


The Attempt at a Solution


To proof what I have to proof I need to draw some help lines. As for instance the "red" one I did from A to B. However I'm very unsure how to write this in mathematical symbols that I draw a helpline to form a triangle ABC (If you imagine that the intersection between A and B is called C.

Any tips on how to write this in a neet mathematical way?
 
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Answers and Replies

  • #2
blue_leaf77
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The line connecting A and B is called chord. According to this, you can write it as ##\textrm{crd }\theta## where ##\theta## is the sector angle subtending the chord. Nevertheless, I think you can also denote it as ##\overline{AB}##.
 
  • #3
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The AB written with a line over is the angle that that the "ARC" ab forms with the midpoint. So I think the crd theta is better option here.

Thanks a lot for the help man :)

(If other people think otherwise they can also reply if you want :P)
 
  • #4
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I might need to write it without using "crd theta" though. Because I don't think I will use the theta angle. I more wanna write "I draw the help line.. to form a triangle"
 
  • #5
blue_leaf77
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The AB written with a line over is the angle that that the "ARC" ab forms with the midpoint.
If I am allowed to be more pedantic, I should deny that because as you can see in this link, an arc between two points looks like the way it's shown there.
I more wanna write "I draw the help line.. to form a triangle"
IMO, saying "chord AB" will not create an ambiguous meaning in your writing.
 
  • #6
Nidum
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" Consider an imaginary line drawn between points A and B . If this line is bisected at point C then .........
 
  • #7
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I have never seen chord or crd, interesting though. The notations I know in geometry are ##\overline{AB}## for the straight through ##A## and ##B## or ##\overline{ABD}## if there is another point ##D## on it, ##\stackrel{\mbox{$\frown$}}{AB}## for the arc between them and ##\angle{ACB}, \; \sphericalangle{ACB} ## or ##\measuredangle{ACB}## for the angle at ##C## between the straights ##\overline{CA}## and ##\overline{CB}##. Parallels are ##\overline{AD}\; \| \; \overline{CB}## and ##\perp## denotes perpendicularity.
 
  • #8
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∠ACB,∢ACB∠ACB,∢ACB\angle{ACB}, \; \sphericalangle{ACB} or ∡ACB
What is the difference between these 3 notations for angles?
 
  • #9
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What is the difference between these 3 notations for angles?
None. Simply a matter of taste. I like the second one, the first might be for the lazy. However, I've seen the first one often in technical drawings.
 

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