Mathematical proof (Drawing a help line)

[Dousin12]

Homework Statement

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

Homework Equations

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?

 

[blue_leaf77]

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 $\overline{AB}$.

 

[Dousin12]

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)

 

[Dousin12]

I might need to write it without using "crd theta" though. Because I don't think I will use the theta angle. I more want to write "I draw the help line.. to form a triangle"

 

[blue_leaf77]

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 want to write "I draw the help line.. to form a triangle"

IMO, saying "chord AB" will not create an ambiguous meaning in your writing.

 

[Nidum]

" Consider an imaginary line drawn between points A and B . If this line is bisected at point C then ...

 

[fresh_42]

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.

 

[Dousin12]

∠ACB,∢ACB∠ACB,∢ACB\angle{ACB}, \; \sphericalangle{ACB} or ∡ACB

What is the difference between these 3 notations for angles?

 

[fresh_42]

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.