Fundamental_Concepts.txt

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Author:
ghstechnology
ID:
82457
Filename:
Fundamental_Concepts.txt
Updated:
2011-04-28 08:23:55
Tags:
Geometry
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Description:
Geometry
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  1. directed line
    one direction is (+) & other (-)
  2. directed line segment
    segment of line containing any 2 points & in between
  3. directed distances
    distances in figure denoted
  4. undirected distances
    length of segment (+)
  5. x-coordinate
    abscissa
  6. y-coordinate
    ordinate
  7. inclination
    • angle greater than or equal to zero degrees
    • formed from a line & (+) x-axis
    • positive direction (rotation CCW)
  8. slope
    • ratio
    • rise/run=change y/change x
    • m=tan theta
  9. formula for angle between two lines
    tan theta=m2-m1/1+m2m1
  10. rules for an angle between two lines
    • psi must be in CCW
    • m1 must be initial side
    • m2 must be terminal side
  11. formula for division of line segment
    ratio= part length/total length
  12. scalene triangle coordinate proof
    (0,0) (a,0) (b,c)
  13. isosceles triangle coordinate proof
    (0,0) (a,0) (a/2,b)
  14. right triangle coordinate proof
    (0,0) (a,0) (0,b)
  15. equilateral coordinate proof
    (0,0) (a,0) (a/2, a/2 root 3)
  16. parallelogram coordinate proof
    (0,0) (a,0) (b,c) (a+b,c)
  17. rectangle coordinate proof
    (0,0) (a,0) (0,b) (a,b)
  18. square coordinate proof
    (0,0) (a,0) (0,b) (a,a)
  19. trapezoid coordinate proof
    (0,0) (a,0) (b,c) (d,c)
  20. isosceles trapezoid coordinate proof
    (0,0) (a,0) (b,c) (a-b,c)
  21. rhombus coordinate proof
    (0,0) (a,0) (b, root a2 - b2) (a+b, root a2 - b2)
  22. quadrilateral coordinate proof
    (0,0) (a,0) (b,c) (d,e)

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