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