REMARKS ON W QUESTION #4


Circled numbers on your paper refer to these.

1)  You can't use Prop. 3.21, or the concept "<" or "less than" 
for angles, because this lemma is needed to prove 3.21 and to 
make sense of that notion.

2)  To be a true analogue of Prop. 3.12, the formulation of your 
lemma should use INTERIOR RAYS, not angles or interior points.  

3)  True, Axiom C-4 immediately give existence AND UNIQUENESS of 
the ray.  The hard part is showing that it is INTERIOR to the 
second angle.

4)  One can prove the lemma by mimicking the proof of 3.12.  
However, it is easier and clearer to USE 3.12 together with the 
crossbar theorem and SAS.  In this second method you don't need 
C-4 at all.

5)  Please pay some attention to how your essay starts.  Clearly 
state what you are trying to achieve, preferably not by quoting 
the command "Formulate and prove ...", and not by featuring an 
exact quotation of 3.12 and then burying your new lemma into a 
long paragraph.

6)  If sleuthing on the web shows up a solution, remember that 
the instructions were different that time.  Slavish copying may 
produce the disaster it deserves.