Quiz

Why specifically along the perpendicular?

It's the shortest path to the edge. It's easy to show that in my scheme, it's enough to prevent the ant from escaping the trap. If the ant is attached to a corner, the spider will eventually be able to reduce the distance to the corner.
Let's say the ant crawls along the edge from the corner. Then the spider slides down from the bisector and goes to intercept. The ant hasn't changed direction => it's caught. The ant decided to crawl in the opposite direction (towards the vertex) => the spider returns to the bisector and still manages to get closer to the vertex in the process. Something like that.