How would I join the two faces as below?:

Two faces

Using knife, I cut the long edge adjacent to the trapezoid to add vertices, and I also successfully used TinyCAD to add vertices in the same place, but I'm still not able to select only the adjacent edge between the two faces. I can only select the entire edge of the rectangle, not just the adjacent portion. Many thanks in advance if any ideas!

  • $\begingroup$ So you want to join the two faces but not at the corners? $\endgroup$ – YoeyYutch May 7 '19 at 4:53

Selecting the top edge of the trapezium is most easily done in Vertex mode - select both ends and switch back to Edge mode. But even then, TinyCad is a bit of a long way round, here.

Vertices must somehow be cut (topologically) into the bottom edge of the rectangle, so alternatives include:

  • With Snap set to 'Active' and 'Vertex' and Automerge switched on:
  • AltD duplicate the bottom vertices of the rectangle in their edge, and drag them any old where..
  • Snap them onto the top vertices of the trapezium

enter image description here

On the whole though, when modeling, you would want the extra edges in the rectangle. If so..

  • CtrlR and scroll, cut 2 edge-loops into the rectangle
  • With Snap and Automerge set as before, and your Pivot set to 'Median', in Vertex mode, with one of the new loop vertices active...
  • SX the new loops, snapping to one of the top vertices of the trapezium.

enter image description here

These are by no means the 'right' ways of doing this.. I'm sure you have/will have your own grab-bag of favorite modeling patterns.

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  • $\begingroup$ Many thanks, and much appreciated Robin and @Israel Bamidele. Unfortunately, as I'm a beginner, I'm having trouble following your instructions (my fault, not yours!). For starters, I'm unable to perform loop-cuts in the rectangle, only the trapezium. Do you know why it's not letting me add loop-cuts to the rectangle? (In case it matters, in Object Mode, I can't select the trapezium and rectangle separately. When I click on one, the conjoined shape is selected. Does that mean that I've inadvertently joined the 2 shapes, and if so, could that be interfering with my loop-cut operations?) $\endgroup$ – Crowdpleasr May 7 '19 at 15:24
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    $\begingroup$ I figured out the loop-cut issue. I had an extra vertex in the rectangle that was throwing things off . . . Now, onto the rest of the exercise! . . . $\endgroup$ – Crowdpleasr May 7 '19 at 15:36

Another easy way is to make 2 "loop cut" like the last image in the previous answer.

After that, switch to "vertex mode", also turn on " all vertex visible"

Press C to switch to "circle select", select the 1st vertex interception and press ALT M to merge the vertex. Do the same for the 2nd vertex interception.

That should solve the problem

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