# Fundamental Concepts

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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)