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Across 4. doesn't rely on anything but postulates 7. if 2 points lie in a plane, then the line containing these 2 points lies in the same plane 8. objects of the set 11. 3 distinct noncollinear points lie in exactly one plane 12. a statement that can be shown to be true by a logical progression of previous terms and statements 14. don't rely on other postulates 15. a visual representation of sets 19. don't contradict one another 20. are the foundation to our system of geometry 23. spot; no dimension; a location in space 24. a group or collection of objects denoted by braces and labeled with a capital letter 29. points that do not lie on the same plane 30. all elements in the universal set not in the given set 35. operations on a single set 36. points that lie on the same line 38. accurate and reversible 42. sets with one-to-one correspondence 43. when two sets have nothing in common 44. any 2 points in space lie in exactly one line 45. something that forces a decision apart from or in opposition to reason

Down 1. neutral; avoids limitations of time or place 2. straight; extends infinitely in one direction; length, no width or thickness 3. flat, extends infinitely in two dimensions 5. if 2 planes intersect, then their intersection is exactly one line 6. to the point; no ambiguous or vague language 9. coplanar lines that do not intersect 10. a line contains 2 points; a plane contains 3 noncollinear points; space contains 4 noncoplanar points 11. planes in space that do not intersect 13. process of justifying a theorem 16. set that contains no elements 17. a system of definitions, postulates, and theorems that is built in a logical progression 18. lines that intersect at a single point 21. lines that lie in the same plane 22. assumed to be true 24. lines that are not coplanar 25. How many points are required for something to be noncollinear 26. model based on 5 incidence postulates 27. points that lie in the same plane 28. refers to processes that require two sets 31. what makes a good geometry 32. denoted by "U" 33. interrelation or sequence of facts or events when seen as inevitable or predictable 34. good grammar, good sentence, only necessary words 37. repeat the pattern established by the last 3 elements 39. sets with the exact same elements 40. using words previously defined or commonly accepted as undefined 41. another name for a postulate