How do I connect a line to a square corner while keeping a clean corner?

I am trying to make a simply perspective cube in Adobe Illustrator. I know there is a way to make it with the perspective grid, but I would prefer to make it using two offset squares. With the offset squares, I am trying to connect each respective corner using the pen tool. When I do this it creates an unclean corner. I have checked, and my smart guides and snap to pixel are both on, and both anchor points line up perfectly. How do I fix these corners?