posted by Shadi .
If [angle]D is a right angle and lines PN, FG, and BD are parallel to each other, prove
[angle]SPN ~ [angle]SFG ~ [angle]SBD
They are all using angle S, which means it doesn't matter how long you extend the top and bottom lines they will always be the same triangle. All three corresponding angles are the same, which makes all three triangles similar.