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Understanding Basic Geometric Concepts: Points, Lines, Segments, and Planes

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This chapter provides a comprehensive overview of the foundational concepts in geometry, including the definitions and properties of points, lines, line segments, rays, and planes. It introduces important postulates and theorems, such as the Segment Addition Postulate and the Angle Addition Postulate, that are essential for understanding geometric relationships. Additionally, it covers the notation used to describe various geometric figures and emphasizes the significance of coplanarity and intersections. This knowledge forms a crucial basis for further studies in geometry.

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Understanding Basic Geometric Concepts: Points, Lines, Segments, and Planes

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  1. CHAPTER 1 REVIEW

  2. POINT M Point M

  3. Lines Lines have infinite amount of points O N M

  4. A B Notation: AB or BA not CB, CA, BC or AC ! A Line segment consists of two endpoints and all the points between those endpoints. C

  5. M L Ray : part of a line consisting of ONE endpoint and all points on one side of the line . A named LM or LA (not AM, MA or ML !)

  6. Planes M Plane M J OR H Plane JHK Plane JKH K Plane KJH Plane KHJ Plane HKJ Plane HJK Plane MKJ

  7. What does each symbol mean? line AB AB AB ray AB segment AB no symbol means length length of segment AB

  8. A R P Practice – What’s in a name? List all of the possible names for each shape <ARP <PRA <R <RAP <ILO <OLI <L <LIO I O 1 N 2 L Name this angle

  9. Parallel lines – Coplanar lines that never intersect

  10. Segment Addition Postulate If B is between A and C, then AB + BC = AC A B C

  11. Angle Addition Postulate If is between then B X A C

  12. Postulate 5 A line contains at least two points Just a point…all alone, no line  P Two points are needed to make a line!

  13. Postulate 5 A plane contains at least three points not all in one line. A B C

  14. Postulate 5 Space contains at least four points not all in one plane.

  15. Postulate 6: through any two points, there is only ONE line. A F

  16. Postulate 7: Through any three non-collinear points, there is exactly one plane. A B C

  17. Postulate 8 If two points are in a plane, then the line that contains the points is in that plane B A

  18. m Postulate 9: two planes intersect in a line. P K

  19. Theorem 1-1: If two lines intersect, then they intersect in exactly ONE POINT ! A

  20. Theorem 1-2 Through a line and a point not in the line, there is exactly one plane. A B C

  21. Theorem 1-3 If two lines intersect, then exactly one plane contains the lines B A D C

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