When using a perpendicular director, why must the compass opening be greater than 1/2 the length of the segment

Because you want to draw 2 arcs ( by putting the point of the compass on each end of the line ) that intersect . If the opening was 1/2 or less than 1/2 of the length they would not intersect.

this is a very good question

step-by-step explanation:

i got a hair cut today from my mom not to flex just to flex kim jon un is one rad fellow i'd say you'd need to take the hairline in kinda like a box shape like someone rammed a lego brick into your head. from there you really need to take the top up keeping with that boxy aesthetic, finally coat the whole thing with gel if your country economics are failing or whatever you can just coat it with the starving children's food rations. about 5 orphans per strand is a good ratio. good luck with the fresh cut my dude