The Intersection tool can be used to create or restore corner points between two straight path segments. To use the tool, click on one straight path segment and drag to another straight path segment. the two segments will be extended to their point of intersection and a corner anchor point will be created. Any path segments between the two on which you click/drag are deleted. The Intersection tool can also be used on open paths (but not two individual paths).
NOTE: The Intersection tool cannot be used with parallel line segments since parallel lines have no logical point of intersection.
Remember that the path segments will be extended to their point of intersection, even if that is away from the open end of an open path. One or both original path segments may be shortened to terminate at the point of intersection.
Use the Shift key with the Intersection tool to create a new object that consists entirely of the area added by the Intersection tool. (The original object is deleted.) A blue preview will show the resulting object. Using the Shift key with the Intersection tool on an open path results in a new open path.
Example: