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1.1: The Building Blocks of Geometry

1.1: 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. Undefined Terms. 1. 2.

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1.1: The Building Blocks of Geometry

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  1. 1.1: 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. 1.1: The Building Blocks of Geometry

  2. Undefined Terms 1. 2. 3. 1.1: The Building Blocks of Geometry

  3. Points 0 dimensional (have no size) Models of points -Dots -Stars in the sky -Cities on a map 1.1: The Building Blocks of Geometry

  4. Points Naming points - Use capital letters A 1.1: The Building Blocks of Geometry

  5. Lines Perfectly straight extending infinitely without thickness. 1 dimensional Models of Lines - roads - hallway - edge of a box 1.1: The Building Blocks of Geometry

  6. Naming Lines l Line l 1.1: The Building Blocks of Geometry

  7. B A Line AB or BA Naming Lines 1.1: The Building Blocks of Geometry

  8. Planes Infinite, flat surface without thickness. 2 dimensional Models of Planes • desktop • rooftop • wall 1.1: The Building Blocks of Geometry

  9. Drawing Planes 1.1: The Building Blocks of Geometry

  10. Naming Planes R Plane R 1.1: The Building Blocks of Geometry

  11. Q P R Naming Planes Plane PQR, PRQ, RPQ, RQP, QRP or QPR 1.1: The Building Blocks of Geometry

  12. A B C Collinear Points Defn:Three or more points are collinear iff they are on the same line. A, B and C are collinear. 1.1: The Building Blocks of Geometry

  13. Coplanar Points Defn: Four or more points are coplanar iff they are on the same plane. 1.1: The Building Blocks of Geometry

  14. Q S P R Coplanar Points P, Q, R and S are coplanar points. 1.1: The Building Blocks of Geometry

  15. 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. 1.1: The Building Blocks of Geometry

  16. Segments A B AB This is not a segment!!! 1.1: The Building Blocks of Geometry

  17. A B The segment with endpoints A and B: denoted AB or BA Segments 1.1: The Building Blocks of Geometry

  18. 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. 1.1: The Building Blocks of Geometry

  19. Z Y The ray with endpoint Y containing Z: denoted YZ (may not be denoted ZY or ZY). Rays 1.1: The Building Blocks of Geometry

  20. 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. 1.1: The Building Blocks of Geometry

  21. Angles 1.1: The Building Blocks of Geometry

  22. sides of the angle vertex of the angle Angles 1.1: The Building Blocks of Geometry

  23. Naming an Angle There are 3 ways to name an angle: ( represents an angle) • The vertex. 2. A point from each side and the vertex (vertex is between the other points). 3. A number. 1.1: The Building Blocks of Geometry

  24. Naming Angles A C 1 B 1.1: The Building Blocks of Geometry

  25. Naming Angles A C 1 B B 1.1: The Building Blocks of Geometry

  26. Naming Angles A C 1 B  ABC or CBA 1.1: The Building Blocks of Geometry

  27. Naming Angles A C 1 B  1 1.1: The Building Blocks of Geometry

  28. 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. 1.1: The Building Blocks of Geometry

  29. Postulates A postulate is a statement that is accepted as being true without proof. 1.1: The Building Blocks of Geometry

  30. Complete Activity 1.1 on page 12. You may work in pairs. 1.1: The Building Blocks of Geometry

  31. Intersecting Lines Postulate • If two lines intersect, then their intersection is a point. 1.1: The Building Blocks of Geometry

  32. Intersecting Planes Postulate • If two planes intersect, then their intersection is a line. 1.1: The Building Blocks of Geometry

  33. 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.” 1.1: The Building Blocks of Geometry

  34. Unique Plane Postulate • Through any 3 noncollinear points there is a unique plane. 1.1: The Building Blocks of Geometry

  35. Flat Plane Postulate • If two points are in a plane, then the line containing them is in the plane. 1.1: The Building Blocks of Geometry

  36. 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. 1.1: The Building Blocks of Geometry

  37. Assignment: pages 14 – 15, # 9 – 48 1.1: The Building Blocks of Geometry

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