2. 1/18/20161.1: The Building Blocks of Geometry Expectation: G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems.

3. 1/18/20161.1: The Building Blocks of Geometry Undefined Terms 1. 2. 3.

4. 1/18/20161.1: The Building Blocks of Geometry Points Models of points 0 dimensional (have no size) -Dots -Stars in the sky -Cities on a map

5. 1/18/20161.1: The Building Blocks of Geometry Points Naming points - Use capital letters A

6. 1/18/20161.1: The Building Blocks of Geometry Lines Perfectly straight extending infinitely without thickness. Models of Lines - roads - hallway - edge of a box 1 dimensional

7. 1/18/20161.1: The Building Blocks of Geometry Naming Lines l Line l

8. 1/18/20161.1: The Building Blocks of Geometry Naming Lines A B Line AB or BA

9. 1/18/20161.1: The Building Blocks of Geometry Planes Infinite, flat surface without thickness. 2 dimensional Models of Planes -desktop -wall -rooftop

10. 1/18/20161.1: The Building Blocks of Geometry Drawing Planes

11. 1/18/20161.1: The Building Blocks of Geometry Naming Planes Plane R R

12. 1/18/20161.1: The Building Blocks of Geometry Naming Planes Plane PQR, PRQ, RPQ, RQP, QRP or QPR P R Q

13. 1/18/20161.1: The Building Blocks of Geometry Collinear Points Defn:Three or more points are collinear iff they are on the same line. ABC A, B and C are collinear.

14. 1/18/20161.1: The Building Blocks of Geometry Coplanar Points Defn: Four or more points are coplanar iff they are on the same plane.

15. 1/18/20161.1: The Building Blocks of Geometry Coplanar Points P, Q, R and S are coplanar points. P R Q S

16. 1/18/20161.1: The Building Blocks of Geometry Segments Defn: A segment is a part of a line that begins at one point and ends at another. The points are called the endpoints of the segment.

17. 1/18/20161.1: The Building Blocks of Geometry Segments AB AB This is not a segment!!!

18. 1/18/20161.1: The Building Blocks of Geometry Segments AB The segment with endpoints A and B: denoted AB or BA

19. 1/18/20161.1: The Building Blocks of Geometry Rays Defn: A ray is a part of a line that starts at a point and extends infinitely in one direction. The point is called the endpoint of the ray.

20. 1/18/20161.1: The Building Blocks of Geometry Rays Y Z The ray with endpoint Y containing Z: denoted YZ (may not be denoted ZY or ZY).

21. 1/18/20161.1: The Building Blocks of Geometry Angles Defn: An angle is a figure formed by two rays with a common endpoint. The common endpoint is called the vertex of the angle and the two rays are called the sides of the angle.

22. 1/18/20161.1: The Building Blocks of Geometry Angles

23. 1/18/20161.1: The Building Blocks of Geometry Angles vertex of the angle sides of the angle

24. 1/18/20161.1: The Building Blocks of Geometry Naming an Angle There are 3 ways to name an angle: (  represents an angle) 1.The vertex. 2. A point from each side and the vertex (vertex is between the other points). 3. A number.

25. 1/18/20161.1: The Building Blocks of Geometry Naming Angles A B C 1

26. 1/18/20161.1: The Building Blocks of Geometry Naming Angles A B C BB 1

27. 1/18/20161.1: The Building Blocks of Geometry Naming Angles A B C   ABC or  CBA 1

28. 1/18/20161.1: The Building Blocks of Geometry Naming Angles A B C  11 1

29. 1/18/20161.1: The Building Blocks of Geometry Intersect and Intersections If 2 figures share one or more points, then they intersect. The point or points they have in common is called their intersection.

30. 1/18/20161.1: The Building Blocks of Geometry Postulates A postulate is a statement that is accepted as being true without proof.

31. 1/18/20161.1: The Building Blocks of Geometry Complete Activity 1.1 on page 12. You may work in pairs.

32. 1/18/20161.1: The Building Blocks of Geometry Intersecting Lines Postulate If two lines intersect, then their intersection is a point.

33. 1/18/20161.1: The Building Blocks of Geometry Intersecting Planes Postulate If two planes intersect, then their intersection is a line.

34. 1/18/20161.1: The Building Blocks of Geometry Unique Line Postulate Through any two distinct points, there is a unique (one and only one) line. Sometimes this is stated in an alternate form: ”Two points determine exactly one line.”

35. 1/18/20161.1: The Building Blocks of Geometry Unique Plane Postulate Through any 3 noncollinear points there is a unique plane.

36. 1/18/20161.1: The Building Blocks of Geometry Flat Plane Postulate If two points are in a plane, then the line containing them is in the plane.

37. 1/18/20161.1: The Building Blocks of Geometry Dimension Postulate Given a line in a plane, there is at least one point in the plane that is not on the line. Given a plane in space, there is at least one point in space not on the plane.

38. 1/18/20161.1: The Building Blocks of Geometry Assignment: pages 14 – 15, # 9 – 48