proving lines are parallel and using slope

a vertical and a horizontal line

are alway perpendicular

2 vertical lines

are always parallel

parallel postulate revised

given a line and a coplanar point not on that line exists exactly one line through the given point parallel to the given lines

converse of the corresponding angle postulate

if 2 lines are cut by a transversal such that corresponding angles are congruent, then the lines are parallel

2 non-vertical lines are perpendicular

if and only if the product of their slopes is 0

2 non-vertical lines are parallel

if and only if they have the same slope

converse of exterior angle theorem

if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel

converse of the alternate interior angle theorem

if two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel

converse of the consecutive interior angle theorem

if two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel

slope

m/ is of a nonvertical line in the coordinate plane containing (x1,y1) and (x2,y2)/ rise over run/ changes in y over changes in x

m

slope

vertical line

slope undefined

equation of a vertical line

x=...

b

y intercept

point-slope form

y-y1=m(x-x1)

y intercept form

y=mx+b