Wait, what are you saying now? That length can be negative, or that it can’t?
Oh, and that shit with the spheres… blargh
Nerds are scary.
Two ridiculously easy proofs.
Given:
13x-2y=3
25x-11y=1
Prove: The solution to the system of equations is (1/3, 2/3)
AND
Did you have to choose to make a system with a bunch of fucking prime numbers? 
The proof is just plugging them in though.
13/3 - 4/3 = 3 → 13 - 4 = 9
25/3 - 22/3 = 1 → 25 - 22 = 3
The line one…
Assume they’re parallel.
If they are, <EXY = <XYF, so we need to show that.
<AXD = <BXE
<AXD + <DXE = pi
<BXE + <BXA = pi
<DXE = <BXA
<BXA = <EXY, I forget why, but they’re opposite angles in intersecting lines.
<XYF = <DXE = <BAX = <EXY
<XYF = <EXY, QED
Geeze…that’s…a little disconcerting.
Uh…I can derive things…that’s kinda cool, I guess…
But what you guys are doing confuses the crap out of me. That’s what I get for being too lazy to read the first 3 pages. 
But can you write them in Satement/Reasoning form?
The first one hardly needs reasoning, they just happen to be equal.
The geometry one, here:
<AXD = <BXE | Given
<AXD + <DXE = pi | Definition of a line
<BXE + <BXA = pi | Definition of a line
<DXE = <BXA | Transitive property
<BXA = <EXY | Vertical angles are congruent
<XYF = <EXY | Transitive property <XYF = <DXE = <BAX = <EXY
AE || FY | Two parallel lines intersected by a transversal form corresponding pairs of angles that are congruent.
(I made a mistake writing it earlier, now fixed)
eww radians
…But that’s the point of a proof…
Proving arithmetic is retarded.
I could prove that those are the ONLY solutions, I guess.