Exercises 1-4, answer true or false and indicate what is wrong with the false statements.

1. Analytic geometry was invented before the development of finite geometries.

Ans: True. Solution:Analytic geometry was invented by Descarte around 1637, while finite geometries were first introduced by Fano in the 1850's.

2. The latter part of the nineteenth century witnessed a revival of interest in the classical geometry of the circle and the triangle, with emphasis on proof in the spirit of the ancient Greeks.

Ans: True.

3. Traditional college geometry of the post-World War II era included the study of more different geometries than are included today.

Ans: False. Solution: Traditional college geometry only included the study of Euclidean geometry.

4. Dynamic geometry is a geometry of movement rather than the static geometry of a set of points.

Ans: True.

Exercises 5-10, draw a figure to explain the following axioms of Hilbert.

5.Order Axiom 2

Solution:

6. Order Axiom 4.

Solution:

7. Order Axiom 5

Solution:

8. Congruence Axiom 3.

Solution:

9. Congruence Axiom 4

Solution:

10. The axiom of continuity.

Solution:

For exercises 11-13, name the axioms of Hilbert that:

11. State Pasch's Axiom.

Ans:II. 5

12. Guarantee the uniqueness of a line joining two distinct points.

Ans: I.1 and I.2

13. Deal with betweeness for points on a line.

Ans:II. 1-4.