1. ## Parellel lines,

Hi,

Why does it naturally follow from

$tan (\alpha - \beta) = \frac{tan \alpha - tan \beta}{1+ tan \alpha tan \beta}$

That lines having the same slope are parellel?
Apparently the same applies for cot and perpendicular lines.

I don't see it.

Thanks
Regards
Craig.

2. Let a and b be the angle each line makes with the horizontal

The slope of a line m = dy/dx = tan(a) or tan(b)

if the lines have the same slope tana = tanb

therefore tan(a-b) = 0

a-b = 0

a = b

i.e the lines are parallel as they make the the same angle with respect to the horizontal