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directed line
one direction is (+) & other (-)
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directed line segment
segment of line containing any 2 points & in between
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directed distances
distances in figure denoted
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undirected distances
length of segment (+)
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inclination
- angle greater than or equal to zero degrees
- formed from a line & (+) x-axis
- positive direction (rotation CCW)
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slope
- ratio
- rise/run=change y/change x
- m=tan theta
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formula for angle between two lines
tan theta=m2-m1/1+m2m1
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rules for an angle between two lines
- psi must be in CCW
- m1 must be initial side
- m2 must be terminal side
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formula for division of line segment
ratio= part length/total length
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scalene triangle coordinate proof
(0,0) (a,0) (b,c)
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isosceles triangle coordinate proof
(0,0) (a,0) (a/2,b)
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right triangle coordinate proof
(0,0) (a,0) (0,b)
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equilateral coordinate proof
(0,0) (a,0) (a/2, a/2 root 3)
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parallelogram coordinate proof
(0,0) (a,0) (b,c) (a+b,c)
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rectangle coordinate proof
(0,0) (a,0) (0,b) (a,b)
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square coordinate proof
(0,0) (a,0) (0,b) (a,a)
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trapezoid coordinate proof
(0,0) (a,0) (b,c) (d,c)
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isosceles trapezoid coordinate proof
(0,0) (a,0) (b,c) (a-b,c)
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rhombus coordinate proof
(0,0) (a,0) (b, root a2 - b2) (a+b, root a2 - b2)
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quadrilateral coordinate proof
(0,0) (a,0) (b,c) (d,e)
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