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1.2 Geometry Definitions

Explore geometric definitions, symbols, and postulates, with examples to deepen understanding in segments, angles, coplanar and collinear points. Learn the Segment and Angle Addition Postulates for further insight. Enhance your knowledge through practical problems and theorems. Challenge yourself with questions involving coplanar points, intersecting lines, and planes. Discover the beauty of geometry through interactive learning!

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1.2 Geometry Definitions

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  1. 1.2 Geometry Definitions

  2. Geometry Symbols

  3. Definitions • Collinear- ________________________________ • Non-Collinear- ____________________________ • Coplanar- ________________________________ • 4. Distance- ________________________________ • __________________________________________ -11 23

  4. 5. Segment- _____________________________ _______________________________________ 6. Ray- _________________________________ Opp Ray- _____________________________ _______________________________________ 7. Congruent- ___________________________ 8. Midpoint- _____________________________

  5. 9. Bisector- _____________________________________ -____________________________________ -____________________________________

  6. 10. Angle- _____________________________________ Acute: _____________________________ Obtuse: ____________________________ Right: ______________________________ Straight: ____________________________

  7. 11. Vertical Angles- ____________________________ _______________________________________________ 12. Adjacent Angles: ___________________________ _______________________________________________ 13. Supplementary- ________________________ 14. Complementary- _______________________ 15. Perpendicular- _____________________________ 1 2

  8. 16. Plane-__________________________________ _____________________________________________ Note: ___________________________________ _________________________________________ _________________________________________ _________________________________________

  9. Examples 1. There is a Right angle at each corner of PRST. a) if angle TPO=60: RPO= ? b) if angle PTO=70: STO= ? c) if angle TOP=50: POR= ? T S O P R

  10. If CBD DBE and BD bisects CBE find • CAB= ? C D X+10 X+5 60 A B E

  11. 3. Solve for y in terms of x. 2 1

  12. D A B C

  13. J F G H

  14. C 1 2 3 B A

  15. 1.3 and 1.4 Segment and Angle Addition Postulates

  16. Define First: • Definition: _________________________ • Postulate: ___________________________________ • ___________________________________ • Theorem- ___________________________________ • ___________________________________

  17. Segment Addition Postulate _______________________________________________ _______________________________________________ _______________________________________________ A B C If B is between A and C then:

  18. Angle Addition Postulate _______________________________________________ _______________________________________________ C B B O A A O C If B lies on the interior of angle AOC then: or

  19. Examples B is between A and C, with AB=x and BC=2x+5. If AC=35: Find x and BC A B C

  20. K L 2 3 1 M A T

  21. 1.5 Postulates &Theorems

  22. You do not need to memorize the numbers, just know what the theorem or postulate says! • Postulate 5 - • ______________________________________ • ______________________________________ • _____________________________________

  23. Postualte 6: • _______________________________________ • ________________________________________ • Postualte 7: • ________________________________________ • __________________________________________ • __________________________________________ • Postualte 8: • _________________________________________ • __________________________________________

  24. Postualte 9: • _____________________________________ • ______________________________________ • Theorem 1.1: • ______________________________________ • _______________________________________ • Theorem 1.2: • _____________________________________ • ______________________________________

  25. Theorem 1.3: • ______________________________________ • _______________________________________ • _______________________________________ • Theorem 1.4: • _______________________________________ • ________________________________________ • ________________________________________ • ________________________________________

  26. Is TW on plane m? • Are TSW coplanar? • Are RWY coplanar? • Where does XY intersect • plane m? • How many lines contain point T and S? • How many planes contain T, S and X? x m T S o R W y

  27. Where do planes R & S intersect? A R B s Name 3 lines that intersect E? Name 2 planes that intersect at FG? Name 2 planes that don’t intersect? Are points RSGC coplanar? S R G H E F D C A B

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