Update on the 120 degree triangle

In the piece that I uploaded to my website (mathcelebration) a few days back, about a property that triangles with a $120^{\circ}$ angle possess, I made the following remark: 


"The pure geometry proof given above is very finely dependent on the hypotheses, and is difficult to generalize (this is a common feature of many such geometric proofs)."


I have just found that this somewhat off the cuff remark was not justified; in fact I have found a pure geometry proof of the converse proposition of that article.


That is, I have found a "pure geometry" way of showing this proposition: if $\angle A$ is not equal to $120^{\circ}$ then $\angle QPR$ is not a right angle. And to my surprise it is a very easy proof!


Here are the links:

• Triangle120degree2Screen
  
• Triangle120degree2PDF

Do have a look at them!