I'd like for the corner circled in red to touch the edge. I tried "up to vertex" extrude but the figure keeps going over instead of coincident.
An edge is not a vertex, so what SolidWorks does is extrude up to the vertex at the end of the edge which is why the extrude over. Without your model I cannot offer a possible better solution but I will offer one based on what I can see.
I recommend creating a second sketch and sketch a line from the corner of your extrude that you want to stop at the edge. Now you extrude up to the vertex of sketched line.
So vertex's are only points not lines?
In SolidWorks land yes. If you go to "extrude propertymanager" in SolidWorks help you will see what SolidWorks is expecting you to select.
When you select an edge, SolidWorks selects the end of the edge closest to where you selected (the red arrow indicates where I selected the edge.
Is vertex my only option? Could I have used "blind" or "up to surface'?
Blind is you only other option except it will not be exact (you should have tried up to surface before asking your question).
As I stated in an earlier reply, without your model or a better screen shot it is difficult to give you what I think would be your best modeling option (I also do not know your design intent of the overall part).
As an example, you could make your sketch off the top face with one corner of the sketch rectangle on the edge and extrude upward (upward, is that allowed to say in SolidWorks?)..
After going over the post again I would suggest this method as the first option, but it all depends on the design intent.
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