I'm trying to cut a shape in QGIS with a set of lines that don't form a single continuous path - they define an edge without holes, but they overlap each other rather than terminating at exactly the start of the next line. I cannot figure out how to use these to cut a polygon - even if I merge the lines, the polygon isn't cut.
Below is a (bad) basic depiction of what I want. Note that the two lines are separate (though in the same multiline layer), and neither extends across the entire width of the polygon.
How can I accomplish the above?