Sketch six points A,B,C,D,E and F, no three of which are collinear. Name the lines defined by these points. How many lines are there?

To sketch the six points A, B, C, D, E, and F, follow these steps:

1. Take a blank sheet of paper or use any drawing software.
2. Mark six distinct points on the paper. You can choose any location and label them as A, B, C, D, E, and F.
3. Ensure that no three points are in a straight line.

The lines defined by these points can be determined by connecting any two points.

For example, to identify the lines:

1. Connect points A and B, and name it line AB.
2. Connect points A and C, and name it line AC.
3. Connect points A and D, and name it line AD.
4. Connect points A and E, and name it line AE.
5. Connect points A and F, and name it line AF.
6. Connect points B and C, and name it line BC.
7. Connect points B and D, and name it line BD.
8. Connect points B and E, and name it line BE.
9. Connect points B and F, and name it line BF.
10. Connect points C and D, and name it line CD.
11. Connect points C and E, and name it line CE.
12. Connect points C and F, and name it line CF.
13. Connect points D and E, and name it line DE.
14. Connect points D and F, and name it line DF.
15. Connect points E and F, and name it line EF.

By following this process, you will end up with a sketch showing the six points and the lines connecting them.

Now, let's count the number of lines. Given six points, we can choose any two points to form a line.

Using the combination formula, we can determine the number of ways to select two points out of six:

C(6,2) = 6! / (2!(6-2)!) = 6! / (2!4!) = (6*5) / (2*1) = 15

Hence, there are 15 distinct lines that can be formed by the six points A, B, C, D, E, and F.