In an incidence geometry where the betweenness axioms hold, prove that for any 2 distinct points A and B, there must exist a point C such that A*C*B. Hint: this question is half proof and half construction. You will need to draw a diagram of the situation. Assemble this proof from the given information (below), and place the statements and their reasons in the correct order in the chart. Statements Reasons 1. given 2. (11) 3. 4. 5. 6. z. 8. definition of a line segment 9. 10. Statements Each statement has a label (A-J) associated to it; use this letter label in the 1st column of the T- chart proof. A. Point F is not in BE B. Line n doesn't meet BE C. There exists a point D not onl. D. Let l be the line A and B are on. E. Let n be the line D and Fare on. F. A and B are points, where A + B. G. Line n meets AE at D and BF at F. H. There exists a point where A * D * E. 1. There exists a point F where E * B * F. J. Line 1 must meet AB at some point C such that A * C * B. Reasons For the reasons, copy exactly what is written. Do not use your own way to name these reasons. definition (11), (12), or (13) prop 6.1 (B1), (B2), (B3), or (B4) In an incidence geometry where the betweenness axioms hold, prove that for any 2 distinct points A and B, there must exist a point C such that A*C*B. Hint: this question is half proof and half construction. You will need to draw a diagram of the situation. Assemble this proof from the given information (below), and place the statements and their reasons in the correct order in the chart. Statements Reasons 1. given 2. (11) 3. 4. 5. 6. z. 8. definition of a line segment 9. 10. Statements Each statement has a label (A-J) associated to it; use this letter label in the 1st column of the T- chart proof. A. Point F is not in BE B. Line n doesn't meet BE C. There exists a point D not onl. D. Let l be the line A and B are on. E. Let n be the line D and Fare on. F. A and B are points, where A + B. G. Line n meets AE at D and BF at F. H. There exists a point where A * D * E. 1. There exists a point F where E * B * F. J. Line 1 must meet AB at some point C such that A * C * B. Reasons For the reasons, copy exactly what is written. Do not use your own way to name these reasons. definition (11), (12), or (13) prop 6.1 (B1), (B2), (B3), or (B4)