Help with understanding Young's Derivation

[aeromat]

Homework Statement

Here they are deriving the equation for Young's experiment: http://www.physicsclassroom.com/Class/light/U12L3c.cfm

The part where they start bringing up "Assertion" and "Logic/Rationale" is where I got confused:
They mention for part ii) that if the distance L >>> y, then S1P is || (parallel) to BP.

iii

S1P = BP

If S1P and BP are || and line S1B is perpendicular to BP, then the length BP = length S1P.

If they are parallel to each other, wouldn't the two lines NOT connect together to form a triangle? What I know about parallel lines, they never intersect, and in this case, they are intersecting at P.

Homework Equations

Young's Equation for a double slit experiment

 

[cepheid]

They're not actually parallel, they're just close enough to parallel that you can pretend that they are parallel (without significant loss of accuracy). It's an approximation. The larger you make L in comparison to y, the "thinner" the triangle gets, and the better this approximation is.