How to connect a few vertices with one edge?

The topology of this element is not good. I need to make more edges. How can I connect all these vertices to the edge on top? I think there is a better option than Knife Tool. Somebody knows?

Video problem HERE

You could delete th big n-gon, select the whole lower vertices and extrude them upward, scale median pint to zero in Z and move upward snapping to the upper location…
or select it; set 3D cursor and scale to 0 in Z… to position it…

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  1. Cut both ends.
  2. Delete the face in the middle, select the edge, align it with extrude/scale (Z+0), and then use the snap to align it at the top.
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I did it. Now the only question is: how can I connect vertices snapped to an edge so that they are inseparable from it?

if you want nice quads everywhere.
1- first you missed some vertices on the sides of your arc in the bottom.

since you have the same thing happening in the order side

2- delete the top faces.

3- select your new vertices you just extruded and extrude them again in Z to meet the top (you can use snapping options)

same thing on the other side

4- then you can use bridge edge loop (cause you will have the same verticies in the other side). or select the edge on the side and keep hitting F to fill

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