Connecting vertices passing through an edge

Very basic problem, but I cannot figure this out and cannot find any tutorials.
In a subdivided rectangle I am trying to connect inside vertices and create faces but when I create 2 edges that meet in the middle they do not create a vertex where they meet.
Any suggestions?

The ‘tinyCAD’ add-on (bundled with Blender, you only need to activate it) has the ability to create vertices at edge intersections. Activate the add-on, select both edges, open the search menu, search for ‘autoVTX’ and invoke it.

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How fantastic!!! Thank you!!!