I'm suppose to: Draw an angle and mark the region of points P for which the following holds: there is no line that intersects the sides of the angle and goes through P
I can't see how this is possible since I believed that you could draw a line through any two points (obviously wrong, but how?). I've looked through my book college geometry and can't find any explanation for this.
In the picture is the solution after talking to my professor, the marked areas are where the points exists that only intersect one of the sides of the angle ABE: Picture of solution
I've included an image of the solution in my original post. if there is some angle ABE, where the ray AB intersects the poincare disk in C, and ray BE intersects the poincare disk in G. Then draw a line from C to G. All the points between that line and the Poincare disk's outer circle won't intersect both rays BA and BE.
also extend the ray to a line so that line BA intersects the poincare disk in D and line BE intersects the poincare disk in F (behind the angle). Then the points between BF, BD and the Poincare disk's outer circle segment won't intersect both rays BE and BA.
Image of solution is in my original post.