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directed line
one direction is (+) & other ()

directed line segment
segment of line containing any 2 points & in between

directed distances
distances in figure denoted

undirected distances
length of segment (+)



inclination
 angle greater than or equal to zero degrees
 formed from a line & (+) xaxis
 positive direction (rotation CCW)

slope
 ratio
 rise/run=change y/change x
 m=tan theta

formula for angle between two lines
tan theta=m_{2}m_{1}/1+m_{2}m_{1}

rules for an angle between two lines
 psi must be in CCW
 m_{1} must be initial side
 m_{2} must be terminal side

formula for division of line segment
ratio= part length/total length

scalene triangle coordinate proof
(0,0) (a,0) (b,c)

isosceles triangle coordinate proof
(0,0) (a,0) (a/2,b)

right triangle coordinate proof
(0,0) (a,0) (0,b)

equilateral coordinate proof
(0,0) (a,0) (a/2, a/2 root 3)

parallelogram coordinate proof
(0,0) (a,0) (b,c) (a+b,c)

rectangle coordinate proof
(0,0) (a,0) (0,b) (a,b)

square coordinate proof
(0,0) (a,0) (0,b) (a,a)

trapezoid coordinate proof
(0,0) (a,0) (b,c) (d,c)

isosceles trapezoid coordinate proof
(0,0) (a,0) (b,c) (ab,c)

rhombus coordinate proof
(0,0) (a,0) (b, root a^{2}  b^{2}) (a+b, root a^{2}  b^{2})

quadrilateral coordinate proof
(0,0) (a,0) (b,c) (d,e)

