# Mathematical proof (Drawing a help line)

1. May 14, 2016

### Dousin12

1. The problem statement, all variables and given/known data
I'm doing quite a strict proof in school. Where we should proof something and use mathematical language and symbols.
2. Relevant equations

3. 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?

Last edited by a moderator: May 15, 2016
2. May 14, 2016

### 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 $\overline{AB}$.

3. May 14, 2016

### 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)

4. May 14, 2016

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

5. May 14, 2016

### blue_leaf77

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

6. May 14, 2016

### Nidum

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

7. May 15, 2016

### Staff: Mentor

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. May 15, 2016

### Dousin12

What is the difference between these 3 notations for angles?

9. May 15, 2016

### Staff: Mentor

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.