Geometry Proof Questions.?

Question

State the postulate that can be used to show each statement is true. Use this link to show the figure needed.
http://img239.imageshack.us/img239/1822/geographproofpv9.png

8. Given that points R and Q lie in plane H, line b also lies in plane H.

9. Line b and XT intersect at T.

10. Points R, Q, and S are coplanar.

11. X and T are collinear.

12. X, T, Q are coplanar.

13. Z and T are collinear.

14. Imagine the following scenario: Point R is the midpoint of PQ and Q is the midpoint of RS. Write a proof to show that PR QS.

Answer 1

8. If two points lie on a plane, the line containing them also lies on the plane.

9. Does T lie on line b? If not, then his is not true.

10. Through three noncolinear points, there is exactly one plane.

11. Unique Line Assumption: Through any two points, there is exactly one line.

12. Through three noncolinear points, there is exactly one plane.

13. Unique Line Assumption: Through any two points, there is exactly one line.

14. PR = RQ and RQ = RS
These are the definitions of midpoints.
PR = RS
This is the reflexive theorem. Two things equal to another thing are equal to each other.

Answer 2

First of all any two points are colinear, and any three points are coplanar. But I'll address your last question.

R is the midpoint of PQ nad Q is the midpoint of RS. I guess you want proof that all four points are colinear.

Let m = gradient of PQ. Since R is on PQ,
m = gradient or RQ
Let n = gradient of RS
since Q is on RS, n = gradient of RQ
Hence n = m.
This proves that PRQ and QS are parallel. Since they have common points, then they are also colinear.