Plane Separation Postulate Proof

[vanrichten]

We learned about half plane geometry today and I am having a hard time with this proof:

\(\displaystyle \mbox{Let }\, l\, \mbox{ be a line and }\, H\, \mbox{ be one of the half-planes}\)

\(\displaystyle \mbox{bounded by }\, l.\, \mbox{Prove that }\, H\, \cup\, l\, \mbox{ is a convex}\)

\(\displaystyle \mbox{set. [Hint: There are four cases to consider.]}\)

Any help is appreciated.

 

[stapel]

We learned about half plane geometry today and I am having a hard time with this proof:

\(\displaystyle \mbox{Let }\, l\, \mbox{ be a line and }\, H\, \mbox{ be one of the half-planes}\)

\(\displaystyle \mbox{bounded by }\, l.\, \mbox{Prove that }\, H\, \cup\, l\, \mbox{ is a convex}\)

\(\displaystyle \mbox{set. [Hint: There are four cases to consider.]}\)

What are your thoughts? What results (theorems, definitions, etc) have been covered in class, that might be helpful? What have you tried so far?

Please be complete, so we can "see" where you are. Thank you!